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AN prNXHx <r$<CjNprNXHx <r$<CjNANd&<x*<NvJBfNFA툾NprNXHx <r$<CjNANd&<x*<NvJBfNGBprNXHx <r$<CjNAhN ANd&<x*<NvJBfNGvANprNXANd&<x*<NvJBfNHNHxNj | L'imprimante est-elle prete ?HPNvoui|nonr"_ NANANd&<x*<NvJBfNHNN\NpNZpNprNp"<NpNNzpNVAN NzANd&<x*<NvJBfNH|AJN ANd&<x*<NvJBfNI8AN A 0AZNdA NA N`/A N`CLN8CNA N`/A N`C튂N8CNA N`/A N`CRN8C@NNF`NqNqANd&<x*<NvJBfNIAN prNXHx <r$<CjNprNXHx <r$<CjNprNXHx <r$<CjNA 0ANd&<x*<NvJBfNJ|A N prNXHx <r$<CjNprNXHx <r$<CjNprNXHx <r$<CjNA 0ANd&<x*<NvJBfNKAN prNXHx <r$<CjNprNXHx <r$<CjNprNXHx <r$<CjNA 0ANd&<x*<NvJBfNKAbN prNXHx <r$<CjNprNXHx <r$<CjNprNXHx <r$<CjNA 0ANd&<x*<NvJBfNLbA,N prNXHx <r$<CjNprNXHx <r$<CjNprNXHx <r$<CjNA 0ANd&<x*<NvJBfNMA4jN prNXHx <r$<CjNprNXHx <r$<CjNprNXHx <r$<CjNA 0ANd&<x*<NvJBfNMA=N prNXHx <r$<CjNprNXHx <r$<CjNprNXHx <r$<CjNA 0AN`C0NzHPNv introduction d'une fonction 4"_N2JBfNNA톨NAN A톨NA C톨NAN`C0NzHPNj propos des agrandissements "_N2JBfNN~A톨NA.N A톨NA C톨NAN`C0NzHPNv propos des rductions e"_N2JBfNNA톨NA N A톨NA C톨NAN`C0NzHPNj quitter le programme "_N2JBfNOHxNv-Souhaitez vraiment quitter| |ce programme ? |HPNvnon|oui4r"_ NANANd&<x*<NJBfNONN NAN A톨NpN"pNpNpNprN <"<NppN" <r$<H <r$<H <r$< H <r$<HNj*INTRODUCTION DE LA FONCTION AVEC LA SOURISHPA N <r$<H <r$<H <r$< H <r$<HNj&INTRODUCTION DE LA FONCTION AU CLAVIERHPA N NzNNH <r$<L8N&<x*<NJBfNRNNH <r$<L8N&<x*<NJBfNQN$fNQA 0NRNNH <r$<L8N&<x*<NJBfNRN$fNRA 0ANdzNJBgNvAN`~N RJi A톨NA C톨NN NAhN AN pNpNpNpN <^"<Np|N NpNpNpNp Np("<^NNj ABS = valeur absolue de ........NpF"<^NNj INT = partie entire de ........Npd"<^NNj SQR = racine carre de .........N <"<^NNj SIN = sinus de .................N <"<^NNj COS = cosinus de ...............N <"<^NNj TAN = tangente de ..............N <"<^NNj ATN = arctangente de ...........N <"<^NNj LN = logarithme nprien de ...N <"<^NNj EXP = exponentielle de .........NpNpNpNpNNNH <r$< L8N&<x*<NpJBgp/NNH <r$<L8N&<x*<NpJBgp/N$fNVpN"pNpNpN <,"<N <@"<NNppN <,"<N <@"<NNppN"AN pN <J"<N <"<NppNpNpNpN <^"<Np|N NNNH <r$<L8N&<x*<NpJBgp/NNH <r$<L8N&<x*<NpJBgp/N$fNXHmRA "_NNd&<x*<NvpJBgp/ADNdzNvpJBgp$fN`A ClNN`HmA "_NNd&<x*<NvpJBgp/HmRA "_N2pJBgp$fNaA ClNNbZA> 0Bm 0BmNd&<x*<NvJBfNc(A ClNNdA> 0AFNHPp(N "_N2JBfNcHm.AZNd&<x*<NN N "_N,C.NAZN`/tC퉌NAZNHmRp-N "_N,CRNA> 0Bm 0BmNp-rLNppN"p(rBNpBN NpN"pFr2NNj"I NT = partie entire de ........Np7r-NpKr=NppN"pFr2NpIN NpN"pdr2NNj"S Q R = racine carre de .........NpUr>NpirLNppN"pdrBNpQN NpN" <r2NNj"S IN = sinus de .................Npsr-N <r=NppN" <r2NpSN NpN" <r2NNj"C OS = cosinus de ...............N <r-N <r=NppN" <r2NpCN NpN" <r2NNj"T AN = tangente de ..............N <r-N <r=NppN" <r2NpTN NpN" <r2NNj"A TN = arctangente de ...........N <r-N <r=NppN" <r2NpAN NpN" <r2NNj"L N = logarithme nprien de ...N <r-N <r=NppN" <r2NpLN NpN" <r2NNj"E XP = exponentielle de .........N < r-N <r=NppN" <r2NpEN NpN"pNpNpNpN <r$<H <r$<H <r$< H <r$<HNvVALIDER = ENTER4HPA N <r$<H <r$<H <r$< H <r$<HNjANNULER = DELETEHPA N N\NHPA "_N2JBgNClNHmlpN "_N2JBfNojpNpNpN <,"<N <@"<NNppN"AN pN <J"<N <"<NppNpNpNpN <^"<Np|N NHmlp N "_N2JBfNqHmRA "_N2JBfNoA C.NA ClNHmRA "_NNd&<x*<NvpJBgp/ADNdzNvpJBgp$fNw(A ClNNwHmA "_NNd&<x*<NvpJBgp/HmRA "_N2pJBgp$fNxA ClNNylA> 0Bm 0BmNd&<x*<NvJBfNz@A ClNN{A> 0AFNHPp(N "_N2JBfNzHm.AZNd&<x*<NN N "_N,C.NAZN`/tC퉌NAZNHmRp-N "_N,CRNA> 0Bm 0BmATNdHAN C턼A 0ATN`CN8&<x*<NvJBfNATNdHATN CA턼 0ANdJBfNATNdHAN A턼Nd&<x*<NHATN ANdzNvJBfNA턼NdHAnN ANdzNvJBfNANdzNpJBgp/ANdNANLNvpJBgp$fNA 0N8A$NdHAN A턼Nd&<x*<NHATN ANdJBfN8A 0NLA h0N NLA$N A N A턼N C$A 0Bm tAFNA N`C@N8zNJBfNA N`C A턼 0A N`CN8zNvJBfNA 0NA NA N`C@N8&<x*<NvJBfNA N`CFN8zNvJBfNA N`/ <r$<CFNA턼Nd&<x*<NA NxNNNA$NdA NLNJBfNNN NLA$N A N tAFNC$A 0A NdHAN C턼A 0A NA$NdA NLNJBfN@NA N`C@N8&<x*<NJBfNrNA N`C@N8&<x*<NvJBfNA N`CFN8zNvJBfN A N`/ <r$<CFNA턼Nd&<x*<NA NxNNNN NLA$N A$N`C@N8zNJBfNPA$N`C$A턼 0N NA N A 0A N`CN8&<x*<NvpJBgp/A N`CN8&<x*<NvpJBgp$VHgNA NdHAN A N`z <r$<A NLNA턼NxN NN\A N A6N AN pN <r-N <"<SNp <r2N <"<NN$ <r-N <"<SN$pNpNpNpN <rPNNj.JE DOIS EXAMINER DE PLUS PRS CETTE FONCTION .N <rKNNv/ELLE PEUT PRSENTER DES POINTS DE DISCONTINUIT4NANdA퉆NBAtNdC퉆NHxANdC퉆NA 0AdN C턼A 0C턼A 0A NdzNgN\A NdzNvpJBgp/A N`CN8&<x*<NvpJBgp/A N`CN8&<x*<NvpJBgp/A N`CN8&<x*<NvpJBgp/A N`CN8&<x*<NvpJBgp/A N`CN8&<x*<NvpJBgp/A N`CN8&<x*<NvpJBgp$VHgNA N`C A$ 0A NdzNJBfN6A N`CN8&<x*<NvJBfNA N`CN8&<x*<NvJBfNA NdHAN A턼Nd&<x*<NA NxA NdHATN ANdJBfNAhN NA NdHAN ANdzNvJBfNA턼NdHAnN ANdzNvJBfNANdzNpJBgp/ANdNANLNvpJBgp$fNAhN N6A N`CN8&<x*<NvJBfNA NdHATN ANdJBfNAN N6A NdHATN ANdJBfN6AN <r$<A$NLNA Nx`PNzN NAN A*N A0N pC퉆N8HANdL8NAHNxA 0ANdJBfN ,ANdJBfN@NV/- ANdCN/- tC@N - C@N8&<x*<NvJBfNP - CFN8zNvJBfN/- <r$<CFN -R+@ N NP - RCN8ANx - CN8N ~N 4X|ANdJBfN.NV/- ANdCN/- tC@NNN NANd& HPA N`CfNz"_N,NNF`nNqBm|N$fNNN&<x*<NpJBgp/NN&<x*< NpJBgp$fNNN&<x*<NpJBgp/NN&<x*<NpJBgp$fNNNH <r$<L8N&<x*<N"N&<x*<NAxNxAxNdzNJBgAxN`/ACfNA 0 <r$<A NAxN`/A N`/A N`C튂N8Cv~NAxN`/A N`/A N`CLN8C|~NAxN`/A N`/A N`CRN8C튚~NNF`pNqBm,A 0 <r$<A NA N`CfNzHPA "_N HPA N`CfNz"_N,NNF`nNqBm|N$fNNN&<x*<NpJBgp/NN&<x*< NpJBgp$fNNN&<x*<NpJBgp/NN&<x*<NpJBgp$fNNNH <r$<L8N&<x*<N"N&<x*<NAxNxAxNdzNJBgAxN`CfNzHPA "_N2JBfNFNA 0 <r$<A NA N`/AxN`/A N`Cv~NC튂NA N`/AxN`/A N`C|~NCLNA N`/AxN`/A N`C튚~NCRNA N`/AxN`/A N`Cv~NCNA N`/AxN`/A N`C|~NCNA N`/AxN`/A N`C튚~NC@NNF`NqAdN C턼AZ 0AxN`CfNzCNACRNA톨NA C톨NN NNzA(NdzNvJBfNҮNNzNvpJBgp/NHPA "_N2pJBgp$gHxNjNPour cette option , il faut|tout d'abord avoir conserv|au moins une fonction HPNjretourr"_ NANN`AN AN A.N A4N AN AN AN A"N pNpNA퇀NA 0 <r$<A NA N`/A N`C튂N8C튦NA N`/A N`CLN8C튠NA N`/A N`CRN8C튬NNF`NqNqACNA(Nd&<x*<NJBfNA^N AN A투NNJfpNNANNANN/ANdzNpJBgp/ANd&<x*<NpJBgp$gN\NJfA톨NNANNA"NNNANLNzNfpJBgp/NNA"NLNzNfpJBgp$fNNA투NAN`/AN`"NAN`/A"N`"N$A톨NN/ANdANLN&<x*<NpJBgp/ANdA"NLN&<x*<NpJBgp/A"NdzNpJBgp/A"Nd&<x*<NpJBgp$gpNtANdANLNJBfNCA. 0CA 0C.A 0ANdA"NLNJBfNTCA4 0C"A 0C4A" 0ANdANLNHA Nd&<x*<NެL8NAtNxANdANLNHA Nd&<x*<NެL8NANxANdANLNHANd&<x*<NެL8NAXNxA"NdANLNHANd&<x*<NެL8NA^NxANdANLN&<x*< NA NLNެA:NxA"NdANLN&<x*<NANLNެA@NxpNpNpNprN <"<NppNANdANLNA:NLNެA NLN"AFNxAFN`?BgAFN`??<~NA"NdANLNA@NLNެANLN"ALNxBgALN`??<ALN`?~NAFC  "002ALC  "002A:C  "002A@C  "002A툾NA Nd&<x*<NެANxANd&<x*<NANxpNA텦N`NANdJBfNrA,N NJfA툾NAN A 0 <r$<A NA N`/A N`C튂N8CNA N`/A N`CLN8CNA N`/A N`CRN8C@NNF`NqNqpNpNpNpNpNz <^rNNjx = HPAtNdN"_N,N <rrNNjy = HPAXNdN"_N,Np"<0NNjx = HPANdN"_N,Np""<0NNjy = HPA^NdN"_N,NA툾Np NzpNA(Nd&<x*<NJBfNNNzNvpJBgp/NHPA "_N2pJBgp$gHxNv | Une autre courbe ?HPNvoui|nonr"_ NANANd&<x*<NvJBfNA^N AN A툾NNNNzNvpJBgp/NHPA "_N2pJBgp$gHxNj" |Sauvegarde de l'agrandissement ?HPNvoui|non4r"_ NANANd&<x*<NvJBfNܾA툾NprNXHx <r$<CjNA C톨NA 0 <r$<A NA N`/A N`C튦N8C튂NA N`/A N`C튠N8CLNA N`/A N`C튬N8CRNA N`/A N`C튦N8CNA N`/A N`C튠N8CNA N`/A N`C튬N8C@NNF`.NqAdN C턼AZ 0ACNACRNAN AFC  "002ALC  "002A:C  "002A@C  "002A퇀NA C퇀NN NAf(x-a)+b ,etc...)sN <r2NNvC3 : CE N'EST PAS L'EFFET 'ZOOM' puique la dformation verticale est4N <r2NNj6 en gnral diffrente de la dformation horizontaleN <"r2NNvA4 : l'agrandissement n'est pas conserv automatiquement . C'est 4N <6r2NNv% vous de le faire ventuellement .uNpNpNpNpNAN N NpN"pNpNpNprN <"<NppN"pNpNpNp2r-N <^"<]NjpNpNpNp7r(N <c"<XNjpN"pNpNpNpNNvA PROPOS DES RDUCTIONSClNp("<NAlNpNp*"<NAlNpNpNpNpNpnr2NNj:1 : vous avez la possibilit de rduire 4 pages graphiquesN <r2NNv%2 : une seule courbe par page rduiterN <r2NNj>3 : pas de possibilits de superposition ( sinon effacement )N <r2NNv;4 : c'est la fonction en cours qui donnera lieu rduction4N <r2NNj<5 : contrairement 'AGRANDISSEMENT' les pages rduites sontN <"r2NNj conservesNpNpNpNpNAN N NpN"pNpNpNprN <"<NppN"pNpNpNp2r-N <^"<]NjpNpNpNp7r(N <c"<XNjpN"pNpNpNpNNvINTRODUCTION D'UNE FONCTIONHClNp("<NAlNpNp*"<NAlNpNpNpNpNpZrdNpN HPNj RESPECTEZ LES PRIORITS ....."_N,Npxr2NNj6Pour avoir f(x) = il faudra crire (1+X)/(3+X)Npn"<NNv1+x N <"<NNv3+x4N?<?<u?<?<u~N <"<,NNjET NON PAS 1+X/3+XN <rdNpN HPNj VOUS DISPOSEZ DE FACILITS ...."_N,N <r2NNvA1-Pour avoir f(x) = 2*x , if suffit de faire .... 2 X VALIDER4N <"<N <"<N$ <"<N <"<N$ <"<N <"<@N$ <r2NNv;2-Pour une fonction plus complique telle que f dfinie par4N < "<NNvf(x) = 3*sin(tan(abs(x)))eN <"r2NNv) il vous suffira de faire respectivementiN <@"<NNv!3 SIN TAN ABS X VALIDER4N <4"<N <E"<N$ <4"<N <E"<N$ <4"<N <E"<4N$ <4"<mN <E"<N$ <4"<EN <E"<cN$ <4"<N <E"<N$ <Yr2NNv- sans avoir vous soucier des parenthses .4NpNpNpNpNAN N NApN AN N\A톨NA투NNJfpNpNpNpNpNNApNNNANLNHANd&<x*<NެL8NANxpNzBgApN`??<ApN`?~N <r$<ApNLNN r NNjy = HPANdN"_N,NNNApNLNfNJBfNvNRNApNNNANLNHANd&<x*<NެL8NANxA투NBgApN`??<ApN`?~NBgApN`??<ApN`?~N <r$<ApNLNN r NNjy = HPANdN"_N,NN$gpNp NzA톨NA C톨NNzN NAxN N\A톨NpN"pNpNpNprN <"<NppN"pNpNpNp2r-N <^"<]NjpNpNpNp7r(N <c"<XNjpN"pNpNpNpNNjCALCUL DE f(a)ClNp("<NAlNpNp*"<NAlNpNpNpNpNpdr2NNjavec :N <rPNNvf(x) = 4HPA"_N,N <rPNNj a =NpNpNpNpNAL 0BmV <r$<H <r$<H <r$<H <@r$< H <@r$< HAs N CpAH 0tHAnN NzANd&<x*<NvJBfNZHxNvSla fonction n'est pas dfinie|au point a , ou alors il y a|dpassement de capacits4HPNjretourr"_ NANN <rdNNj RPONSE : HPANdN"_N,NpNpNpNpNpN <@rdNNv autre point4N <,rZN <J"<N$ <@"<NNjretourN <,"<N <J"<&N$NJfBm|N$fNNNH <r$<L8N&<x*<NpJBgp/NNH <r$<L8N&<x*<NpJBgp$fNAx 0NNNH <r$<L8N&<x*<NpJBgp/NNH <r$<L8N&<x*<NpJBgp$fNAx 0AxNdzNJBgAxNd&<x*<NvJBfN <"<N <"<@Np <r2N <T"<XNpN\NA톨NA C톨NN NAN AN A N pN"pNpNpNprN <"<NppN"pNpNpNp2r-N <^"<]NjpNpNpNp7r(N <c"<XNjpN"pNpNpNpNNv%COURBE REPRSENTATIVE DE x-->f(x-a)+b4ClNp("<NAlNpNp*"<NAlNpNpNpNpNpZrFNNjavec :N <rZNNvf(x) = 4HPA"_N,N <"<NNva =NpNpNpNpNAL 0BmV <r$<H <r$<H <r$<H <@r$< H <@r$< HAs N CpA 0pNpNpNpN <"<NNvb =4NpNpNpNpN <r$<H <r$<H <r$<H <@r$< H <@r$< HAs N CpA 0A Nd&<x*<NެANxANd&<x*<NANxANdzNvJBfNzA&N NA투NA투NAN ANdJBfNANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxANd&<x*< NvJBfN\ANdAtNLNAtNxA Nd&<x*< NvJBfNANdANLNANxA,N N"ANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxpNpNpNNJfN\A투NANd&<x*< NvJBfNANdBANLN"HANdL8NAtNxA Nd&<x*< NvJBfNANd&<x*< NANLN"HANdL8NANxANdAtNLNANxANdzNvJBfNBmANdANLNANLNgNANdANLNAHNxtHAnN ANdzNvJBfNANdANLNANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNANdANLNANLNެANLNN ?AN`?ANdANLNެANLNN ?ANN`?~NCNA 0A 0NANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNANdANLNެANLNN /ANN`"NA 0CNA 0NBmNBm <Ѝ/ANd _N`vN FBmANd&<x*<NH <r$<L8ANBmAN`C퉆N8HANdvNpL8NAHNxANd&<x*<NN C퉆N8HANdvNpL8NHANdL8AHNtHAnN ANdzNvJBfNANdANLNANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN2ANdAHNLNHANdL8NANLNެANLNN ?AN`?ANdAHNLNANLNެANLNN ?ANN`?~NCNA 0A 0NANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNANdAHNLNANLNެANLNN /ANN`"NA 0CNA 0NBmNBmN`NqANdAHNLNJBfN f(a-x)4ClNpN"pNpNpNprN <"<NppN"pNpNpNp2r-N <^"<]NjpNpNpNp7r(N <c"<XNjpN"pNpNpNpNNv#COURBE REPRSENTATIVE DE x-->f(a-x)4ClNp("<NAlNpNp*"<NAlNpNpNpNpNpdr2NNjavec :N <rFNNvf(x) = 4HPA"_N,N <"<NNva =NpNpNpNpNAL 0BmV <r$<H <r$<H <r$<H <@r$< H <@r$< HAs N CpA 0A Nd&<x*<NެANxANd&<x*<NANxANdzNvJBfN A&N N A투NA투NAN ANdJBfNvANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxANd&<x*< NvJBfN ANdBANLN"HANdNhHANd&<x*< NANLN"L8NL8N AtNxA Nd&<x*< NvJBfNfANdNhHANdANLNL8NHANd&<x*< NANLN"L8N ANxA,N NANdBANLN"HA NdANLNL8N AtNxANd&<x*< NANLN"HANdANLNL8N ANxA투NpNpNpNNJfCtA 0ANdzNvJBfNBmANdANLNgNANdANLNAHNxtHAnN ANdzNvJBfNANdANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNANdANLNANLNެANLNN ?AN`?ANdANLNެANLNN ?ANN`?~NCNA 0A 0NANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNANdANLNެANLNN /ANN`"NA 0CNA 0NBmNBm <Ѝ/ANd _N`NBmANd&<x*<NH <r$<L8ANBmAN`C퉆N8HANdvNpL8NAHNxANd&<x*<NN C퉆N8HANdvNpL8NHANdL8AHNtHAnN ANdzNvJBfNANdANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNAHNdANLNANLNANLNެANLNN ?AN`?AHNdANLNANLNެANLNN ?ANN`?~NCNA 0A 0NANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNAHNdANLNANLNެANLNN /ANN`"NA 0CNA 0NBmNBmN`NqN`NqA 0AZNdA NA N`/A N`CLN8CNA N`/A N`CRN8C@NA N`/A N`C튂N8CNNF`NqNqA투NNzN NN\Nv#COURBE REPRSENTATIVE DE x-->b-f(x)4ClNpN"pNpNpNprN <"<NppN"pNpNpNp2r-N <^"<]NjpNpNpNp7r(N <c"<XNjpN"pNpNpNpNp("<NAlNpNp*"<NAlNpNpNpNpNpZr2NNjavec :N <rFNNvf(x) = 4HPA"_N,N <"<NNvb =NpNpNpNpNAL 0BmV <r$<H <r$<H <r$<H <@r$< H <@r$< HAs N CpA 0A Nd&<x*<NެANxANd&<x*<NANxANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxANdzNvJBfNA&N NA투NA투NAN ANdJBfNA,N A투NpNpNpNNJfCtAH 0ANdzNvJBfNvBmANdAHNLNgNptHAnN ANdzNvJBfNPANdANLNANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNANdAHNLNANLNެANLNN ?AN`?ANdAHNLNެANLNN ?ANN`?~NCNA 0A 0NJANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNFANdAHNLNެANLNN /ANN`"NA 0CNA 0NJBmNTBm f(kx)ClNpN"pNpNpNprN <"<NppN"pNpNpNp2r-N <^"<]NjpNpNpNp7r(N <c"<XNjpN"pNpNpNpNp("<NAlNpNp*"<NAlNpNpNpNpNpdr2NNjavec :N <rFNNvf(x) = 4HPA"_N,N <"<NNvk =NpNpNpNpNAL 0BmV <r$<H <r$<H <r$<HtH <r$<HAs N CpA턤 0A턤NdzNJBfN6 <"<N <"<JNpN6A Nd&<x*<NެANxANd&<x*<NANxANdBANLN"HANdL8N A턤NLN"AtNxANd&<x*< NANLN"HA NdL8N A턤NLN"ANxANd&<x*< NvJBfN7ANdBANLN"AtNxA Nd&<x*< NvJBfN8 ANd&<x*< NANLN"ANxANdzNvJBfN8HA&N N8PA투NA투NpNpNpNNJfCtA 0ANdzNvJBfN;BmANdANLNgN;ANdA턤NLNެAHNxtHAnN ANdzNvJBfN:ANdANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN:>ANdANLNANLNެANLNN ?AN`?ANdANLNެANLNN ?ANN`?~NCNA 0A 0N:ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN:ANdANLNެANLNN /ANN`"NA 0CNA 0N:BmN:Bm <Ѝ/ANd _N`N=: <r$<H <r$<H <r$< H <r$<HNv9C'EST LE SEUL CAS O LA COURBE EST TRACE POINT PAR POINT4HPA N pdNA투NAtNdANLN&<x*< N"ANxAtNdA턤NLNެAHNxANdA턤NLNެHANdL8AHNtHAnN ANdzNvJBfN=0ANdANLNެ&<x*<NެANLNANNxANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN=0A턤NdAHNLNANxANdANLNެANLNN /ANN`"NN`NqA 0AZNdA NA N`/A N`CLN8CNA N`/A N`CRN8C@NA N`/A N`C튂N8CNNF`NqNqA투NNzN NN\Nj"COURBE REPRSENTATIVE DE x-->kf(x)ClNpN"pNpNpNprN <"<NppN"pNpNpNp2r-N <^"<]NjpNpNpNp7r(N <c"<XNjpN"pNpNpNpNp("<NAlNpNp*"<NAlNpNpNpNpNpdr2NNjavec :N <r2NNvf(x) = 4HPA"_N,N <"<NNvk =NpNpNpNpNAL 0BmV <r$<H <r$<H <r$<HtH <r$<HAs N CpA턤 0A턤NdzNJBfN@* <"<N <"<JNpN?A Nd&<x*<NެANxANd&<x*<NANxANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxANdzNvJBfNA A&N NAA투NA투NAN ANdJBfNABA,N A투NpNpNpNNJfCtAH 0ANdzNvJBfNCBmANdAHNLNgNCtHAnN ANdzNvJBfNCANdA턤NLNެANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNC ANdAHNLNANLNެANLNN ?AN`?ANdAHNLNެANLNN ?ANN`?~NCNA 0A 0NCANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNCANdAHNLNެANLNN /ANN`"NA 0CNA 0NCBmNCBm NHmxAcN CpA 0Hm~AcN ANd&p1N "_N2JBfN@Hm8p1N "_NArZN CA^ 0AHNdHANNdHHm8Hm>A^NdAXNLN HAXNdHA^NdHA_.N A^NdAXNLN AHNLN&<x*<NAHNxA턀Nd&<x*<NvJBfN~AHN`/ANN`"Np)N NAHNd&<x*<NAHNxAHN`/ANN`"NAPNAHNd&<x*<NAHNxHmDp0N "_N <r$<AHNLNAHNxADNnHPp-N "_Nf(x) choix d'un repre choix d'un intervalle trac de la courbe d'quation y = f(x) complment sauvegarde de la fonction  rappel d'une fonction sauvegarde du graphique rappel du graphique effacer trac d'une droite agrandissement rappel de l'agrandissement rduction rappel 'page rduite' hardcopy divers rsolution graphique de l'quation f(x) = m calcul de f(a) avec a = ? graphique de x --> f(x-a)+b x --> f(a-x) x --> b-f(x) x --> f(|x|) x --> |f(x)| x --> f(kx) x --> k f(x) remarques introduction d'une fonction propos des agrandissements propos des rductions STOP quitter le programme ***2^HX( , (.J(HNp( lN((4p<,(^ZV~ҀJBB8" j.zN:X@pLhh6P$.d>\HzjB>v.zr,,,,,*,,n^8hvh6P$.,>DHNf @.x"`V&>h"`V&>d"DXhVnH"VHv"."DB$0<<"(D(l64 HD6,, H42:0,,8 D ,  8.D:$8$:@::r:p(bҐ$n$> x~Ddhv" "R\<&Nd."."&0*6V0J 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CN 0`@k Ap0(/.NuA Nup)@JphNLtH &JKBCH .A/~0 1PP1P1PA L? &<@>AFG0000X0000X0000X0000C ~AJ0g0  pi, N"F QNu?S@k&8L &LeBLe,C`(A? fHa)_ 2TNuBlJ`l *bl ,bH .N0S@k@>A PC/~. 0(JgRJ)@g1@CJ2fP2HP" &" *pdN0,r W1@AJ00 piN9|L@NpiN _CL""pe`9| LpiN9|LphNLtH 2H/`SBSC@AHH/jP 6P/^P0<rtN2papapapaL/jr`S@k6@ A 9PJg8BPpfNpgN9| LphN9@JfdBlJa\Q 6BB 2`NuS@k @ A 9pJg a$Bp`NuHS&I. FV 7p&N.9l/h8,:,L/d4,pĴ@cS@9@p4,rŴAcBSA9Ar`8pJ, 7fnJ/^k0 Eg$2,/h pg  qfH9A/hpjN`XHxNj:Ecrit en GFA BASIC et compil.| | Auteur : Michel Coquio |HPNjretourr"_ NANpNJ gN@AN,N pr NXHx <r$<CNprNXHx <r$<CNprNXprNXHx <r$<CNHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNA x0 <r$<A NA N`/p"NXA N`/ <r$<CNNF`NqNqBmBm(ACjNACNAN A 0 <r$<A NA N`/A N`CN8CNA N`/A N`C퉼N8C(NA N`/A N`CN8CNNF`NqNqAN C턼A 0ApN pNJ gN@NAPN NvAN BmpNJ gN@NAN AN pNJ gNBA 0ANdA NA N`/A N`CN8CNA N`/A N`C(N8C퉼NA N`/A N`CN8CNNF`NqNqA*N ARNprNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNA 0pNJ gNBprNXHx <r$<CNprNXHx <r$<CNAN pNJ gNCA0N A 0ANdA NA N`/A N`CN8CNA N`/A N`C(N8C퉼NA N`/A N`CN8CNNF`NqNqApN BmA 0 A z0 pNJ gNDAFNprNXHx <r$<CNpNJ gNDNvBmprNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNpNJ gNENAFNprNXHx <r$<CNprNXHx <r$<CNpNJ gNElAN pNJ gNEAN prNXHx <r$<CNprNXHx <r$<CNApN pNJ gNFAdNprNXHx <r$<CNpNJ gNFVprNXHx <r$<CNAچN pNJ gNFzA|NprNXpNJ gNGHxNj | L'imprimante est-elle prete ?HPNvoui|nonr"_ NANANd&<x*<NvJBfNGN\NpNZpNprNp "<Nppp@pW?<?<NN\pp@pW?<?<NN\pp@pWBg?<NN\pp@pW?<?<NN\pN"prN <"<NpNpNVAN prN <"<NppN"AN NzpNJ gNHAN pNJ gNH.AN pNJ gNHAN prNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNA 0pNJ !gNIRA;pN prNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNA 0pNJ "gNIAFRN prNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNA 0pNJ #gNJvAON prNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNA 0pNJ $gNKA]N prNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNA 0pNJ %gNKAdN prNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNA 0pNJ &gNL,AmN prNXHx <r$<CNprNXHx <r$<CNprNXHx <r$<CNA 0pNJCNzHPNj propos des agrandissements "_N2JBfNLANNA4N ANNA CNNpNJCNzHPNv propos des rductions "_N2JBfNLANNAN ANNA CNNpNJCNzHPNv introduction d'une fonction 4"_N2JBfNMfANNAN ANNA CNNpNJCNzHPNj quitter le programme "_N2JBfNN$HxNv-Souhaitez vraiment quitter| |ce programme ? |4HPNvnon|oui4r"_ NANANd&<x*<NJBfNN$NN NA텦N ANNpN"pNpNpNprN <"<NppN" <r$<H <r$<H <r$< H <r$<HNj*INTRODUCTION DE LA FONCTION AVEC LA SOURISHPAN <r$<H <r$<H <r$< H <r$<HNj&INTRODUCTION DE LA FONCTION AU CLAVIERHPAN NzNNH <r$<L8N&<x*<NJBfNP~NNH <r$<L8N&<x*<NJBfNP N$fNPA텦 0NP~NNH <r$<L8N&<x*<NJBfNP~N$fNP~A텦 0A텦NdzNJBgNvA텦N`~N gPANNA CNNN NA|N pNpNpNpNprN <"<TNjpNprN <"<TNdpNpNpNpNpN <rdNNjf(x) =NpNpNpNpN <"<Np|N NpNpNpNpNpNpNpNpr2NNj"A B S = valeur absolue de ........Np r>NprLNppN"prBNpBN NpN"p#r2NNj"I NT = partie entire de ........Npr-Np&r=NppN"p#r2NpIN NpN"p2r2NNj"S Q R = racine carre de .........Np*r>Np5rLNppN"p2rBNpQN NpN"pAr2NNj"S IN = sinus de .................Np9r-NpDr=NppN"pAr2NpSN NpN"pPr2NNj"C OS = cosinus de ...............NpHr-NpSr=NppN"pPr2NpCN NpN"p_r2NNj"T AN = tangente de ..............NpWr-Npbr=NppN"p_r2NpTN NpN"pnr2NNj"A TN = arctangente de ...........Npfr-Npqr=NppN"pnr2NpAN NpN"p}r2NNj"L N = logarithme nprien de ...Npur-N <r=NppN"p}r2NpLN NpN" <r2NNj"E XP = exponentielle de .........N <r-N <r=NppN" <r2NpEN NpN"pNpNpNpN <r$<H <r$<H <r$< H <r$<HNvVALIDER = ENTER4HPAN <r$<H <r$<H <r$< H <r$<HNjANNULER = DELETEHPAN N\NHPA "_N2JBgNCNHmpN "_N2JBfNWpNpNpN <"<N <"<NNppN"A|N pN <"<N <"<NppNpNpNpN <"<Np|N NHmp N "_N2JBfNY,HmA "_N2JBfNWJA CNA CNHmA "_NNd&<x*<NvpJBgp/ADNdzNvpJBgp$fN^A CNN_ZHmxA "_NNd&<x*<NvpJBgp/HmA "_N2pJBgp$fN`fA CNNaA> 0Bm 0BmNd&<x*<NvJBfNaA CNNctA> 0ANHPp(N "_N2JBfNbHmAZNd&<x*<NN N "_N,CNAZN`/tC2NAZNHmp-N "_N,CNA> 0Bm 0BmNd&<x*<NvpJBgp/ADNdzNvpJBgp$fNsA CNNtHmxA "_NNd&<x*<NvpJBgp/HmA "_N2pJBgp$fNuA CNNv0A> 0Bm 0BmNd&<x*<NvJBfNvA CNNxA> 0ANHPp(N "_N2JBfNwHmAZNd&<x*<NN N "_N,CNAZN`/tC2NAZNHmp-N "_N,CNA> 0Bm 0Bm HPA N`CNz"_N,NNF`nNqBm|N$fNNN&<x*<NpJBgp/NN&<x*< NpJBgp$fNNN&<x*<NpJBgp/NN&<x*<NpJBgp$fNNNH <r$<L8N&<x*<N"N&<x*<NAxNxAxNdzNJBgAxN`/AjCNA 0 <r$<A NAxN`/A N`/A N`C(N8C~NAxN`/A N`/A N`CN8C"~NAxN`/A N`/A N`CN8C@~NNF`pNqBm,A 0 <r$<A NA N`CNzHPA "_N HPA N`CNz"_N,NNF`nNqBm|N$fNNN&<x*<NpJBgp/NN&<x*< NpJBgp$fNNN&<x*<NpJBgp/NN&<x*<NpJBgp$fNNNH <r$<L8N&<x*<N"N&<x*<NAxNxAxNdzNJBgAxN`CNzHPA "_N2JBfNZNA 0 <r$<A NA N`/AxN`/A N`C~NC(NA N`/AxN`/A N`C"~NCNA N`/AxN`/A N`C@~NCNA N`/AxN`/A N`C~NC퉼NA N`/AxN`/A N`C"~NCNA N`/AxN`/A N`C@~NCNNF`NqAN C턼A 0AxN`CNzCjNAjCNANNA CNNN NNzA(NdzNvJBfNNNzNvpJBgp/NHPA "_N2pJBgp$gHxNjNPour cette option , il faut|tout d'abord avoir conserv|au moins une fonction HPNjretourr"_ NANN~AN AN A.N A4N AN AN AN A"N pNpNA&NA 0 <r$<A NA N`/A N`C(N8CLNA N`/A N`CN8CFNA N`/A N`CN8CRNNF`NqNqAjCpNA(Nd&<x*<NJBfNA0N ApN ARNNJfpNNANNANN/ANdzNpJBgp/ANd&<x*<NpJBgp$gN\NJfANNNANNA"NNNANLNzNfpJBgp/NNA"NLNzNfpJBgp$fNN(ARNAN`/AN`"NAN`/A"N`"N$ANNN/ANdANLN&<x*<NpJBgp/ANdA"NLN&<x*<NpJBgp/A"NdzNpJBgp/A"Nd&<x*<NpJBgp$gpNtANdANLNJBfN&CA. 0CA 0C.A 0ANdA"NLNJBfNhCA4 0C"A 0C4A" 0ANdANLNHA Nd&<x*<NެL8NAtNxANdANLNHA Nd&<x*<NެL8NANxANdANLNHANd&<x*<NެL8NAXNxA"NdANLNHANd&<x*<NެL8NA^NxANdANLN&<x*< NA NLNެA:NxA"NdANLN&<x*<NANLNެA@NxpNpNpNprN <"<NppNANdANLNA:NLNެA NLN"AFNxAFN`?BgAFN`??<~NA"NdANLNA@NLNެANLN"ALNxBgALN`??<ALN`?~NAFC  "002ALC  "002A:C  "002A@C  "002AdNA Nd&<x*<NެANxANd&<x*<NANxpNAN`NA텬NdJBfNՆAN NJfAfN AdNAN A 0 <r$<A NA N`/A N`C(N8C퉼NA N`/A N`CN8CNA N`/A N`CN8CNNF`NqNqpNpNpNpNpNz <rNNjx = HPAtNdN"_N,N <rNNjy = HPAXNdN"_N,Np"<0NNjx = HPANdN"_N,Np"<0NNjy = HPA^NdN"_N,NAdNp NzpNA(Nd&<x*<NJBfN NNzNvpJBgp/NHPA "_N2pJBgp$gHxNv | Une autre courbe ?HPNvoui|nonr"_ NANANd&<x*<NvJBfN A0N ApN AdNNNNzNvpJBgp/NHPA "_N2pJBgp$gHxNj" |Sauvegarde de l'agrandissement ?HPNvoui|non4r"_ NANANd&<x*<NvJBfNAdNprNXHx <r$<CNA CNNA 0 <r$<A NA N`/A N`CLN8C(NA N`/A N`CFN8CNA N`/A N`CRN8CNA N`/A N`CLN8C퉼NA N`/A N`CFN8CNA N`/A N`CRN8CNNF`.NqAN C턼A 0ApCjNAjCNAN AFC  "002ALC  "002A:C  "002A@C  "002A&NA C&NN NAN AN A텎N ANNpNtNzHm|A "_Nf(x-a)+b ,etc...)sNpsr2NNvC3 : CE N'EST PAS L'EFFET 'ZOOM' puique la dformation verticale est4Np}r2NNv7 en gnral diffrente de la dformation horizontale4N <r2NNvC4 : l'agrandissement n'est pas conserv automatiquement . C' est 4N <r2NNv% vous de le faire ventuellement .uNAN N NpN"pNpNpNprN <"<NppNpN"pNpNpNpr-N <"<]NjpNpNpNpr(N <"<XNjpN"pNpNpNpNNvA PROPOS DES RDUCTIONSCNp"<NANpNp"<NANpNpNpNpNp7r/NNj:1 : vous avez la possibilit de rduire 4 pages graphiquesNpKr/NNv%2 : une seule courbe par page rduiterNp_r/NNj>3 : pas de possibilits de superposition ( sinon effacement )Npsr/NNv;4 : c'est la fonction en cours qui donnera lieu rduction4N <r/NNvE5 : contrairement AGRANDISSEMENT les pages rduites sont conserves4NAN N NpN"pNpNpNprN <"<NppNpN"pNpNpNpr-N <"<]NjpNpNpNpr(N <"<XNjpN"pNpNpNpNNvINTRODUCTION D'UNE FONCTIONHCNp"<NANpNp"<NANpNpNpNpNp-rdNpN HPNj RESPECTEZ LES PRIORITS ....."_N,NpHxNvSla fonction n'est pas dfinie|au point a , ou alors il y a|dpassement de capacits4HPNjretourr"_ NANNr <rdNNj RPONSE : HPANdN"_N,NpN <rdNNv autre pointN <rZN <"<N$ <"<NNjretourN <"<N <"<&N$NJfBm|N$fNNNNH <r$<L8N&<x*<NpJBgp/NNH <r$<L8N&<x*<NpJBgp$fNAx 0NNNNH <r$<L8N&<x*<NpJBgp/NNH <r$<L8N&<x*<NpJBgp$fNNAx 0AxNdzNJBgAxNd&<x*<NvJBfNpZ"<Npi"<@NppnrN <"<NpN\NANNA CNNN NAN AN pNpNpNprN <"<NppNpNpNpNprxNNv%COURBE REPRSENTATIVE DE x-->f(x-a)+bNpNpNpNpNp2rNNjavec :NpFr2NNvf(x) = 4HPAj"_N,Npd"<NNva =NpNpNpNpNBmPAR 0 <r$<H <r$<H <r$<H <@r$< H <@r$< HA~N CpA 0pNpNpNpN <"<NNvb =4NpNpNpNpN <r$<H <r$<H <r$<H <@r$< H <@r$< HA~N CpA 0A Nd&<x*<NެANxANd&<x*<NANxAfN ANdzNvJBfNA݊N NARNARNApN A텬NdJBfNANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxANd&<x*< NvJBfNANdAtNLNAtNxA Nd&<x*< NvJBfNANdANLNANxAN NLANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxpNpNAN`NNJfN\ARNANd&<x*< NvJBfNANdBANLN"HANdL8NAtNxA Nd&<x*< NvJBfN6ANd&<x*< NANLN"HANdL8NANxANdAtNLNANxA텬NdzNvJBfNBmANdANLNANLNgNANdANLNAHNxtHAN ANdzNvJBfNANdANLNANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN*ANdANLNANLNެANLNN ?AN`?ANdANLNެANLNN ?ANN`?~NCNA 0A 0NANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNANdANLNެANLNN /ANN`"NA 0CNA 0NBmNBm <Ѝ/ANd _N`vNvBmANd&<x*<NH <r$<L8ANBmAN`C,N8HANdvNpL8NAHNxANd&<x*<NN C,N8HANdvNpL8NHANdL8AHNtHAN ANdzNvJBfNANdANLNANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNbANdAHNLNHANdL8NANLNެANLNN ?AN`?ANdAHNLNANLNެANLNN ?ANN`?~NCNA 0A 0NANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNANdAHNLNANLNެANLNN /ANN`"NA 0CNA 0NBmN"BmN`NqANdAHNLNJBfNlANd&<x*<NANxN`NqA 0ANdA NA N`/A N`CN8CNA N`/A N`CN8CNA N`/A N`C(N8C퉼NNF`NqNqNzARNN N\Nv#COURBE REPRSENTATIVE DE x-->f(a-x)4CNpN"pNpNpNprN <"<NppN"pNpNpNp2r-N <^"<]NjpNpNpNp7r(N <c"<XNjpN"pNpNpNpNNv#COURBE REPRSENTATIVE DE x-->f(a-x)4CNp("<NANpNp*"<NANpNpNpNpNpdr2NNjavec :N <rFNNvf(x) = 4HPAj"_N,N <"<NNva =NpNpNpNpNAL 0BmV <r$<H <r$<H <r$<H <@r$< H <@r$< HA~N CpA 0A Nd&<x*<NެANxANd&<x*<NANxANdzNvJBfNA݊N NARNARNANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxApN A텬NdJBfN|AN ANdBANLN"HA NdANLNL8N AtNxANd&<x*< NANLN"HANdANLNL8N ANxARNpNpNpNNJfCtA 0A텬NdzNvJBfN BmANdANLNgN ANdANLNAHNxtHAN ANdzNvJBfN ANdANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN ANdANLNANLNެANLNN ?AN`?ANdANLNެANLNN ?ANN`?~NCNA 0A 0N ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN ANdANLNެANLNN /ANN`"NA 0CNA 0N BmN Bm <Ѝ/ANd _N`N BmANd&<x*<NH <r$<L8ANBmAN`C,N8HANdvNpL8NAHNxANd&<x*<NN C,N8HANdvNpL8NHANdL8AHNtHAN ANdzNvJBfN ANdANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN AHNdANLNANLNANLNެANLNN ?AN`?AHNdANLNANLNެANLNN ?ANN`?~NCNA 0A 0N ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN AHNdANLNANLNެANLNN /ANN`"NA 0CNA 0N BmN BmN`NqN`NqA 0 <r$<A NA N`/A N`CN8CNA N`/A N`CN8CNA N`/A N`C(N8C퉼NNF`NqNqARNNzN\Nv#COURBE REPRSENTATIVE DE x-->b-f(x)4CNpN"pNpNpNprN <"<NppN"pNpNpNp2r-N <^"<]NjpNpNpNp7r(N <c"<XNjpN"pNpNpNpNp("<NANpNp*"<NANpNpNpNpNpZr2NNjavec :N <rFNNvf(x) = 4HPAj"_N,N <"<NNvb =NpNpNpNpNAL 0BmV <r$<H <r$<H <r$<H <@r$< H <@r$< HA~N CpA 0A Nd&<x*<NެANxANd&<x*<NANxANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxANdzNvJBfNA݊N NARNARNApN A텬NdJBfNAN ARNpNpNpNNJfCtAH 0A텬NdzNvJBfNzBmANdAHNLNgNttHAN ANdzNvJBfNTANdANLNANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNANdAHNLNANLNެANLNN ?AN`?ANdAHNLNެANLNN ?ANN`?~NCNA 0A 0NNANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNJANdAHNLNެANLNN /ANN`"NA 0CNA 0NNBmNXBm f(kx)CNpN"pNpNpNprN <"<NppN"pNpNpNp2r-N <^"<]NjpNpNpNp7r(N <c"<XNjpN"pNpNpNpNp("<NANpNp*"<NANpNpNpNpNpdr2NNjavec :N <rFNNvf(x) = 4HPAj"_N,N <"<NNvk =NpNpNpNpNAL 0BmV <r$<H <r$<H <r$<H <r$<H <r$<HA~N CpA턤 0A턤NdzNJBfN*BpZ"<Npi"<JNpN)A Nd&<x*<NެANxANd&<x*<NANxANdBANLN"HANdL8N A턤NLN"AtNxANd&<x*< NANLN"HA NdL8N A턤NLN"ANxANd&<x*< NvJBfN+XANdBANLN"AtNxA Nd&<x*< NvJBfN+ANd&<x*< NANLN"ANxANdzNvJBfN+A݊N N+ARNARNpNpNpNNJfCtA 0A텬NdzNvJBfN.BmANdANLNgN.ANdA턤NLNެAHNxtHAN ANdzNvJBfN.xANdANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN-ANdANLNANLNެANLNN ?AN`?ANdANLNެANLNN ?ANN`?~NCNA 0A 0N.rANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN.nANdANLNެANLNN /ANN`"NA 0CNA 0N.rBmN.|Bm <Ѝ/ANd _N`N0 <r$<H <r$<H <r$< H <r$<HNv9C'EST LE SEUL CAS O LA COURBE EST TRACE POINT PAR POINT4HPAN pdNARNAtNdANLN&<x*< N"ANxAtNdA턤NLNެAHNxANdA턤NLNެHANdL8AHNtHAN ANdzNvJBfN0ANdANLNެ&<x*<NެANLNANNxANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN0A턤NdAHNLNANxANdANLNެANLNN /ANN`"NN`NqA 0 <r$<A NA N`/A N`CN8CNA N`/A N`CN8CNA N`/A N`C(N8C퉼NNF`NqNqARNNzN\Nj"COURBE REPRSENTATIVE DE x-->kf(x)CNpN"pNpNpNprN <"<NppN"pNpNpNp2r-N <^"<]NjpNpNpNp7r(N <c"<XNjpN"pNpNpNpNp("<NANpNp*"<NANpNpNpNpNpdr2NNjavec :N <r2NNvf(x) = 4HPAj"_N,N <"<NNvk =NpNpNpNpNAL 0BmV <r$<H <r$<H <r$<H <@r$< H <@r$< HA~N CpA턤 0A턤NdzNJBfN3pZ"<Npi"<JNpN3A Nd&<x*<NެANxANd&<x*<NANxANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxANdzNvJBfN4A݊N N4ARNARNApN A텬NdJBfN4AN ARNpNpNpNNJfCtAH 0A텬NdzNvJBfN7BmANdAHNLNgN7|tHAN ANdzNvJBfN7\ANdA턤NLNެANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN6ANdAHNLNANLNެANLNN ?AN`?ANdAHNLNެANLNN ?ANN`?~NCNA 0A 0N7VANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fN7RANdAHNLNެANLNN /ANN`"NA 0CNA 0N7VBmN7`Bm f(a-x)NpNpNpNpNp2rNNjavec :NpFr2NNvf(x) = 4HPAj"_N,Npd"<NNva =NpNpNpNpNBmPAR 0 <r$<H <r$<H <r$<H <@r$< H <@r$< HA~N CpA 0AfN A Nd&<x*<NެANxANd&<x*<NANxANdzNvJBfN=lA݊N N=tARNARNApN A텬NdJBfN?6ANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxANd&<x*< NvJBfN>ANdBANLN"HANdNhHANd&<x*< NANLN"L8NL8N AtNxA Nd&<x*< NvJBfN?&ANdNhHANdANLNL8NHANd&<x*< NANLN"L8N ANxAN N?ANdBANLN"HA NdANLNL8N AtNxANd&<x*< NANLN"HANdANLNL8N ANxARNpNpNAN`NNJfCtA 0A텬NdzNvJBfNBBmANdANLNgNBANdANLNAHNxtHAN ANdzNvJBfNBhANdANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNAANdANLNANLNެANLNN ?AN`?ANdANLNެANLNN ?ANN`?~NCNA 0A 0NBbANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNB^ANdANLNެANLNN /ANN`"NA 0CNA 0NBbBmNBlBm <Ѝ/ANd _N`NEBmANd&<x*<NH <r$<L8ANBmAN`C,N8HANdvNpL8NAHNxANd&<x*<NN C,N8HANdvNpL8NHANdL8AHNtHAN ANdzNvJBfNEANdANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNDAHNdANLNANLNANLNެANLNN ?AN`?AHNdANLNANLNެANLNN ?ANN`?~NCNA 0A 0NEANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNEAHNdANLNANLNެANLNN /ANN`"NA 0CNA 0NEBmNEBmN`NqN`NqA 0ANdA NA N`/A N`CN8CNA N`/A N`CN8CNA N`/A N`C(N8C퉼NNF`NqNqARNNzN NpNpNpNprN <"<NppNpNpNpNN\prxNNv#COURBE REPRSENTATIVE DE x-->b-f(x)NpNpNpNpNp2rNNjavec :NpFr2NNvf(x) = 4HPAj"_N,Npd"<NNvb =NpNpNpNpNBmPAR 0 <r$<H <r$<H <r$<H <@r$< H <@r$< HA~N CpA 0AfN A Nd&<x*<NެANxANd&<x*<NANxANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxANdzNvJBfNHA݊N NHARNARNApN A텬NdJBfNHAN ARNpNpNAN`NNJfCtAH 0A텬NdzNvJBfNKBmANdAHNLNgNKtHAN ANdzNvJBfNKANdANLNANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNJANdAHNLNANLNެANLNN ?AN`?ANdAHNLNެANLNN ?ANN`?~NCNA 0A 0NKANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNKANdAHNLNެANLNN /ANN`"NA 0CNA 0NKBmNKBm f(kx)NpNpNpNpNp2rNNjavec :NpFr2NNvf(x) = 4HPAj"_N,Npd"<NNvk =NpNpNpNpNBmPAR 0 <r$<H <r$<H <r$<HtH <r$<HA~N CpA턤 0A턤NdzNJBfNfpZ"<Npi"<JNpNeAfN A Nd&<x*<NެANxANd&<x*<NANxANdBANLN"HANdL8N A턤NLN"AtNxANd&<x*< NANLN"HA NdL8N A턤NLN"ANxANd&<x*< NvJBfNgANdBANLN"AtNxA Nd&<x*< NvJBfNgANd&<x*< NANLN"ANxANdzNvJBfNh$A݊N Nh,ARNARNpNpNAN`NNJfCtA 0A텬NdzNvJBfNjBmANdANLNgNjANdA턤NLNެAHNxtHAN ANdzNvJBfNjANdANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNj ANdANLNANLNެANLNN ?AN`?ANdANLNެANLNN ?ANN`?~NCNA 0A 0NjANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNjANdANLNެANLNN /ANN`"NA 0CNA 0NjBmNjBm <Ѝ/ANd _N`Nm( <r$<H <r$<H <r$< H <r$<HNv9C'EST LE SEUL CAS O LA COURBE EST TRACE POINT PAR POINT4HPAN AN`NpdNARNAtNdANLN&<x*< N"ANxAtNdA턤NLNެAHNxANdA턤NLNެHANdL8AHNtHAN ANdzNvJBfNmANdANLNެ&<x*<NެANLNANNxANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNmA턤NdAHNLNANxANdANLNެANLNN /ANN`"NN`NqA 0ANdA NA N`/A N`CN8CNA N`/A N`CN8CNA N`/A N`C(N8C퉼NNF`NqNqARNNzN NpNpNpNprN <"<NppNpNpNpNN\prxNNj"COURBE REPRSENTATIVE DE x-->kf(x)NpNpNpNpNp2rNNjavec :NpFr2NNvf(x) = 4HPAj"_N,Npd"<NNvk =NpNpNpNpNBmPAR 0 <r$<H <r$<H <r$<HtH <r$<HA~N CpA턤 0A턤NdzNJBfNoxpZ"<Npi"<JNpNnAfN A Nd&<x*<NެANxANd&<x*<NANxANdBANLN"HANdL8N AtNxANd&<x*< NANLN"HA NdL8N ANxANdzNvJBfNpdA݊N NplARNARNApN A텬NdJBfNpAN ARNpNpNAN`NNJfCtAH 0A텬NdzNvJBfNsTBmANdAHNLNgNsNtHAN ANdzNvJBfNs.ANdA턤NLNެANLNެ&<x*<NެANLNANNxANd&<x*<NvpJBgp/ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNr~ANdAHNLNANLNެANLNN ?AN`?ANdAHNLNެANLNN ?ANN`?~NCNA 0A 0Ns(ANNd&<x*<NpJBgp/ANNd&<x*<NpJBgp$fNs$ANdAHNLNެANLNN /ANN`"NA 0CNA 0Ns(BmNs2Bm f(x) choix d'un repre choix d'un intervalle trac de la courbe d'quation y = f(x) complment sauvegarde de la fonction rappel d'une fonction sauvegarde du graphique rappel du graphique effacer trac d'une droite agrandissement rappel de l'agrandissement rduction rappel 'page rduite' hardcopy divers rsolution graphique de l'quation f(x) = m calcul de f(a) avec a = ? graphique de x --> f(x-a)+b x --> f(a-x) x --> b-f(x) x --> f(|x|) x --> |f(x)| x --> f(kx) x --> k f(x) remarques introduction d'une fonction propos des agrandissements propos des rductions STOP quitter le programme ***2^RJ&xX  J8>`N>($p(X\T~ҀJBB8"jB>v.zr,,,,,*,,n^8hvh6P$.,>DHNf @.~ ^.z.:X@pLhh6P$.d>\Hzl"x"`V&>h"`V&>d"DXhVnH"VHv"."DB$0<<"(D(l64 HD6,, H42:0,,8 D ,  8.D:$8$:@::r:p(bҐ$n$> x~Ddhv" "R\<&Nd."."&0*6V0J ,0,,",<V< V(D X|&<$b"ΐVfLL&<.8.8r&r&b~v&r0FTjfbB Nt0FTjfb(Bt"B B<f^$,$D&2|ZzZzbz&^hpBB2B< |a6RGk0Gg`a(0GVfA1G<ap??<?<NM\Nu??< 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FV 7p&N9l/h8,:,L/d4,pĴ@cS@9@p4,rŴAcBSA9Ar`8pJ, 7fnJ/^k0 Eg$2,/h pg  qfH9A/hpjNܰ`N>A 0 <r$<A NV?<Bg?<O?<MBgB ->/?<NqANr?<Bg?<O?<BgB ->/?<NqANrAN&<x*<N pJBgp/AN&<x*<N pJBgp/AN&<x*<N pJBgp/AN&<x*<N pJBgp$VHg N N2N`NqAN&<x*<N pJBgp/AN&<x*<N pJBgp/AN&<x*<N pJBgp/AN&<x*<N pJBgpF$NqN3HxN$|Cette disquette a |un problemeHPN$finr"_ NANrNd?<NNTUfN4JHxN8 Ce programme ne fonctionne| | qu'en haute rsolution !|HPN$O K4r"_ NAvNrNd)| A CN>A텂N&<x*<N JBfN9AN A CN>AN A텂 0A P0 <r$<A NVA N/p"NXA N/ <r$<C틎NN`NqNqAdN prNXHx <r$<C틎NprNXHx <r$<C틎NA 00 <r$<A NVA N/p"NXA N/ <r$<C틎NN`NqNqpr"NXHx" <r$<C틎NA 0 <r$<A NVA N/p"NXA N/ <r$<C틎NN`NqNqpr0NXHx0 <r$<C틎NANArN pNJ gN<8ArBN pr.NXHx. <r$<C틎NprNXprNXHx <r$<C틎NHx <r$<C틎Npr'NXHx' <r$<C틎NpNJ gN`AgN pr'NXHx' <r$<C틎Npr)NXHx) <r$<C틎NpNJ gN@A 0A$ 0ALN AN A 00 <r$<A NVA N/p"NXA N/ <r$<C틎NN`NqNqA P0 <r$<A NVA N/p"NXA N/ <r$<C틎NN`NqNqpr"NXHx" <r$<C틎Npr%NXHx% <r$<C틎Npr(NXHx( <r$<C틎Npr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎Npr0NXHx0 <r$<C틎Npr'NXHx' <r$<C틎NA텂N&<x*<N JBfN@BmA CN>AN ArN A CN>pNJ gNBA 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpr'NXHx' <r$<C틎Npr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎NAN A 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpNJ gNCvA 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpr'NXHx' <r$<C틎Npr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎NA+*N A 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpNJ gNDA 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpr'NXHx' <r$<C틎Npr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎NA7N A 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpNJ gNFFA 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpr'NXHx' <r$<C틎Npr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎NADN A 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpNJ gNGBmA 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpr'NXHx' <r$<C틎Npr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎NAQ|N A 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpNJ gNIA 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpr'NXHx' <r$<C틎Npr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎NAnN A 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpNJ gNJBmA 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpr'NXHx' <r$<C틎Npr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎NAlN A 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpNJ gNK|A 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpr'NXHx' <r$<C틎Npr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎NA^\N pNJ gNKpr!NXHx! <r$<C틎NAN pNJCNHPN$! donne d'un polynome quelconque "_NJBfNNNDAN AN A P0 <r$<A NVA N/p"NXA N/ <r$<C틎NN`NqNqA 00 <r$<A NVA N/p"NXA N/ <r$<C틎NN`NqNqpr%NXHx% <r$<C틎Npr'NXHx' <r$<C틎Npr(NXHx( <r$<C틎Npr"NXHx" <r$<C틎Npr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎Npr0NXHx0 <r$<C틎NA텂N&<x*<N JBfNNBmA CN>AN ArN pNJ "gNNAN pr'NXHx' <r$<C틎Npr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎NpNJCNHPN courbe d'quation y = P(x) "_NJBfNOA"N Hx. <r$<C틎NHx' <r$<C틎NHx) <r$<C틎NHx& <r$<C틎NALN C$A텠 0CA텦 0C*A 0CA 0ArN A,NpNJ &gNPpr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎NA,NC텠A$ 0C텦A 0CA* 0CA 0A$N&<x*<N JBfNPA 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqA$NHA!N ArN A,NpNJ 'gNQHxN$Imprimante branche ?| yHPN$oui|non4r"_ NANrAN&<x*<N JBfNQpNZpNpNpNprNp"<N,NrpNVANAN pNJ (gNTfpNZA텔 0A$N&<x*<N JBfNRtA 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqA 0A$N&<x*<N JBfNSpC튼NjHpC.NjL8NA킦NpC튼NjHpC.NjL8NANpC튼NjHpC.NjL8NA"NNSpC튼NjHpC.NjL8NA킦NpC튼NjHpC.NjL8NANpC튼NjHpC.NjL8NA"NA"N ArN AJN ArN pNVANHx. <r$<C틎NHx) <r$<C틎NHx. <r$<C틎NHx' <r$<C틎NAN )|8 JNzp NpNpNprNArN pNJ )gNTANpr*NXHx* <r$<C틎NC$A텠 0CA텦 0pNJ *gNUANpr'NXHx' <r$<C틎Npr.NXHx. <r$<C틎NpNJ -gNU\A6N pr'NXHx' <r$<C틎NpNJ .gNUANpr/NXHx/ <r$<C틎NpNJ /gNVpNܸANpr'NXHx' <r$<C틎Npr)NXHx) <r$<C틎NpNJ 1gNVNDpNpNpNprN <"<N,pr'NXHx' <r$<C틎Npr)NXHx) <r$<C틎Npr.NXHx. <r$<C틎NA텂N&<x*<N JBfNVprNXHx <r$<C틎NpNJCNHPN$ calcul de P(a) avec a = ? 4"_NJBfNcA$N&<x*<N JBfNWdAN NcLA 0 <r$<A NVA N/A NCFNjC튼NA N/A NCLNjC.NN`NqNqpNܸpNpNpNprN <"<N,pNpNpNp$r2N <T"<XN&pNp(r-N <Y"<SN&pNܸpN~pNpNpNpZrdNN$Soit calculer P(a) avec :4N>pN~pNpNp NpNܬpN <"<NNP(x) =N> <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN <"<NNa =N>BmA킲 0pNܬ <r$<H <r$<H <r$<H <r$<H <r$<HA9N ACN>ACN>pN <"<N <"<N, <r$<H <r$<HHmHmtHtHtHAQACN>HmAVN CjA톨 0HmAVN CjA텲 0A텲NA톨NN&<x*< NVJBfN\JHxN$9Prenez un nombre raisonnable.| |Limites : -1000 +1000HPN$O.Kr"_ NANrNDpr.NXHx. <r$<C틎NNcpN~ <rdNN$ RPONSE :eN>pN~ <"rdNN$ P(a) =4N>pC.NjHpC.NjL8NBHpC.NjL8NBA텲NNBA텲NNBNCN>HmHmAjvN A텎N&<x*<N JBfN]HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NBmNcA퇞CN>HmpC튼NjHpC.NjL8NBHpC.NjL8NBNHPAjvN A텎N&<x*<N JBfN^HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NBmNcA퇞CN>HmpC튼NjHpC.NjL8NBHpC.NjL8NBA텲NNBNHPAjvN A텎N&<x*<N JBfN_pHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDBmNcHmHmAgN A텎N&<x*<N JBfN` HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDBmpr.NXHx. <r$<C틎NNcAzCN>HmpC튼NjHpC.NjL8NBHpC.NjL8NBA텲NNBA텲NNBNHPAgN A텎N&<x*<N JBfNa,HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NBmNcAzCN>HmHmAmN A텎N&<x*<N JBfNaHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDBmpr.NXHx. <r$<C틎NNcACN>ACN>HmAVN pNܬAN )mNbx <r$<H <r$<HHmHmtHtHtHAQAjNN&AjNNDJBfNcLN$( valeur approche : tHPAN.AjNNN"_NHPN )"_NCN> <T"<NAN>pr'NXHx' <r$<C틎Npr.NXHx. <r$<C틎Npr)NXHx) <r$<C틎NpNJCNHPN quitter le programme "_NJBfNdpHxN$-Souhaitez vraiment quitter| |ce programme ? |4HPN$non|oui4r"_ NAvNrAvN&<x*<NDJBfNdpNdN NdNDpN~pNpNp NAN N NdNDpNܸNzpNpNpNprN <"<N,pNpNp NpNpNprNppNܸpd"<NAN>A 0 <r$<A NVpNܸA N&<x*<N`N/A N&<x*<N`N"NAN>N`NqNqBgBg?<?<A8" NpNܸNzpN~pNpNpNNn quations ( 1 < n < 7 )CN>Np inconnues ( 1 < p < 7 )CN>pNpNpNpNܬ <r$<H <r$<H <r$<H <r$<HA~N <"<NAN>pNpNpNpNܸpN~pNpNp NpNpN?<P?<,?<?<rA" NA 0 <r$<A NV <r$<A NN\&<x*<NB&<x*<N`H <r$<H <r$<HA NHA:N N`~Nq <r$<H <r$<H <r$<HAnN pNܸCxAZ 0pN~pNpNpN <"<NN$n quations n = N> <"<NAZNNN>CZAl 0?<P?<A"N"pNpN <r$<H <r$<H <r$<H <r$<HA~N pN~pNpNpN <"<NAN>pNܸpNpNpN~pNpNp NA 0 <r$<A NV <r$<A NN\&<x*<NB&<x*<N`H <r$<H <r$<HA NHA:N N`~Nq <r$<H <r$<H <r$<HAnN pNܸCxA 0NDA퀖N TA퀐N TA퀜N TA퀢N TA퀨N TA퀮N TA퀺N TpNpNpNprN <|"<vN,pN~pNAZN&<x*<NB&<x*<N\vNXN&&<x*<N`A퀄NAN&<x*<NB&<x*<N\vNXN&&<x*<N`A퀊NAN&<x*<NBA퀊NN`H <r$<L8N\A퀮NA퀮N&<x*<N`A퀺NA 0AZNANVAT 0ANATNVpaNHPp N"_NHPAN&<x*<N`NN"_NHPATN&<x*<N`NN"_NCN>pxNHPp N"_NHPATN&<x*<N`NN"_NCN> <r$<ATNN\&<x*<NBA퀊NN`A퀖N <r$<ANN\&<x*<NBA퀄NN`A퀐NA퀖N&<x*<N`A퀜NC퀐A퀢 0N4A퀖N/A퀐N"NAN~N4A퀜N/A퀢N"NAN~A퀜N&<x*<N`A퀨NATN&<x*<NtpJBgp/ANATNNVpJBgp$fNn~N4A퀨N/A퀐N"Np+NN`NqN4A퀮N/A퀐N"Np=NN4A퀺N/A퀐N"NpbNHPp N"_NHPAN&<x*<N`NN"_NN~AN&<x*<NBN&vNXA퀊NN`A NC퀐AJ 0N`NqpN~pNpNp N <hrdNN6Cofficients et constantes sont des nombres RATIONNELSN>pNܬ?<?<l?<?<l~NAp N pNpNpN <TrN <"<N,AN N NdAZN/ANCD~N.AZN/ANCt~N.AZN/ANCJ~N.AZN/ANCz~N.AZNCPN,AZNCVN,AZNC튀N,AZNC튆N,AZNC튌N,AN&<x*<N`NC튪N,AZN/ANC튞~N.ANC튰N,ANCnN,ANC튶N,A 0ANA NVA N/A NCnNN`NqNqAJN&<x*<N`AJNA 0pNܬA 0AZNANVAT 0AN&<x*<N`ATNVA&N N`NqNqN`NqNqBmN NdAN TAN TNDpNpNN4p r NNN0QUELQUES INSTANTS !NCZA 0A 0AN A큰 0ANAZNN `A큰NVBmA큰NHAN AN&<x*<N JBfNsA큰NA큞NNDJBfNs\C큰Az 0C큞A 0A*N A큰N/A큰NCJ~NANA큰N/A큰NCD~NANA큰NHAN AN NtA큰N&<x*<N`A큒NANA큰NNVJBfNtA큒NHATN AN&<x*<N JBfNtrA큒NHA큰NHA*N NrNtA큒N&<x*<N`A큒NAN&<x*<N`A큒NNVJBfNtNt N`NqANAZNN `A큰N <r$<&<x*<A큰NA큰N/A큰NCD~NzNDJBfNuJAN N`NqNqBmAT 0ANATNVAZN/ATNCD~NzN JBfNuAN&<x*<N`ANN`NqNqANANN JBfNv>AZNCPNjzN JBfNv: <r$<AZNN\AZNNuTNv>BmANAZNNVpJBgp/ANzNDpJBgp$fNvA 0AN&<x*<N`ANNDpNpNN$CVotre systme quivaut au systme dont la matrice est la suivante :CN>AN pN~pNpNp NAT 0ANATNVATNC튶NjH <r$<L8N\N/ <r$<A퀐NN\N"NpxNN>ATNC튶NjH <r$<L8N\N/ <r$<A퀐NN\N"NATNCnNjNN>N`0NqpN~pNpNp NAN~N x^y{zN NdNIl n'a donc pas de solution.CN> <r$<A퀐NN\Nr NAN>A퀐N&<x*<N`H <r$<AZNN\&<x*<NBL8N`Nr NAN>pNܬpNpNprNAtN/ <r$<AZNN\&<x*<NBA퀐NN`&<x*<N`N"NA큌N/ <r$<AZNN\&<x*<NBA퀐NN`&<x*<N`N"NN NdN"Il admet donc une unique solution.CN> <r$<A퀐NN\Nr NAN>A퀐N&<x*<N`H <r$<AZNN\&<x*<NBL8N`Nr NAN>pN <r$<H <r$<H <r$<H <r$<HAz(N AN pN~pNpNp N <r$<A퀐NN\NrdNN$ Que voici ...&N>pNN NdN(Il admet donc une infinit de solutions.CN> <r$<A퀐NN\Nr NAN>A퀐N&<x*<N`H <r$<AZNN\&<x*<NBL8N`Nr NAN>pN <r$<H <r$<H <r$<H <r$<HAz(N AN AZN&<x*<N`ATNANATNVA 0AZNANVAN/ATNCD~NzNVJBfN}ATNC튶NjHAN/ATNC튞~NvNXL8N\H <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"Np-NN>NAN/ATNCD~NzN\JBfNATNC튶NjHAN/ATNC튞~NvNXL8N\H <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"NN N>AZN&<x*<N`ATNN\JBfNATNC튶NjHAN/ATNC튞~NvNXL8N\H <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"Np+NN>AN/ATNCD~NHAN/ATNCJ~NL8NB&<x*<N pJBgp/AN/ATNCD~NzN pJBgp$fNATNC튶NjH <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"NN N>AN/ATNCD~NzNDJBfNATNC튶Nj&<x*<N`N/ <r$<ANN\&<x*<NBA퀐NN`N"NpxNN>ATNC튶Nj&<x*<N`N/ <r$<ANN\&<x*<NBA퀐NN`&<x*<N`N"NATNCnNjNN>N` NqN`NqA 0AZNANVANCPNjzNtJBfN2p+NCN>N@p-NCN>ANC튶Nj&<x*<N`HAN&<x*<N`NC튪NjvNXL8N`AHNANC튰NjvNXAHNN\H <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"NN N>ANC튰NjvNXAHNN\H <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"NAN>N`:NqpN~pNpNp NA퀐N&<x*<N`H <r$<AZNN\&<x*<NBL8N`Nr N <"<N, <r$<A퀐NN\NrdNN$ Que voici ...&N>pNN Nd <r$<A퀐NN\NrN <r$<A퀐NN\N"<N, <r$<A퀐NN\Nr NNL N>A퀐N&<x*<N`H <r$<ANN\&<x*<NBL8N`Nr NA퀐N&<x*<N`H <r$<ANN\&<x*<NBL8N`N"<N,AT 0AZNATNVA 0 <r$<ATNN\ANVATNC튶NjH <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"Np NN>N`~NqATN&<x*<N`ANAZNANVATNC튶NjH <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"Np NN>N`~NqATNC튶NjH <r$<L8N\N/ <r$<ATNN\&<x*<NBA퀐NN`N"NpxNN>ATNC튶NjN/ <r$<ATNN\&<x*<NBA퀐NN`&<x*<N`N"NATNCnNjNN>N`NqpNpNprNpNܬA퀖N&<x*<N`N/ <r$<A퀐NN\N"NA퀖N&<x*<N`N? <r$<A퀐NN\N?A퀖N&<x*<N`N? 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N>pN~pNpNp NN NdA큒 0A큒N&<x*<N JBfN.Bm <r$<ANN\A NVNHNvHA N&<x*<N`NC튶NjL8N\HA N&<x*<N`NC튪NjvNXL8NVpJBgp/N`Nv&<x*<NVpJBgp/NVNv&<x*<N pJBgp$fN A N&<x*<N`A큒NN`Nq`pNܬpNpNprNA큒NC튶Nj&<x*<N`N/ <r$<A퀐NN\N"NA큒NC튶NjHA큒NC튪NjvNXL8N\H <r$<L8N\N/ <r$<AZNN\&<x*<NBA퀐NN`&<x*<N`N"NN NdpNpNprNp*"<N,pN~pNpNp NAT 0ANATNVATNC튶NjH <r$<L8N\N/ <r$<A퀐NN\N"NpxNN>ATNC튶NjH <r$<L8N\N/ <r$<A퀐NN\N"NATNCnNjNN>N`0NqpN~pNpNp NN NdClAZ 0A 0AZNANVAN/ANC튀NjCPNAN/ANC튆NjCVNAT 0ANATNVAN/ATN/AN/ATNCt~NCD~N8AN/ATN/AN/ATNCz~NCJ~N8ATN/ATNCnNN`lNqN`NqN NdLAN ZBmCZA 0 <r$<ANANAN/ANCD~NzNDJBfNBA 0CA큞 0N`NqNqN NdLA큒N ZBmCZA 0 <r$<A큰NANAN/A큒NCD~NzNDJBfNA 0N`NqNqN NdC큰A 0AZNA큰NNVJBfNA큰N&<x*<N`AzNAZNAzNV <r$<H <r$<HAzN/ANCD~NBHAzN/ANCJ~NHAjN N`NqNqN NdC큰A 0A큰N&<x*<NVJBfN <r$<A큰NN\AzN <r$<&<x*<AzN <r$<H <r$<HAzN/ANCD~NBHAzN/ANCJ~NHAjN N`NqNqN NdA튪NAN&<x*<N`NC튪N,AHN TANN TAhN TAnN TAT 0ANATNVBmfBm`A 0AZNANVAN/ATN/AN/ATNCD~NNNNvHAN/ATNCJ~NNNNvL8N C튞~N8ATN/ATNC튪NjHAN/ATNC튞~NL8N C튪NN`6NqATNC튪NjAbNN`AbNN`NqA 0AZNANVAN/ANCPNjNNNvHANCVNjNNNvL8N C튰NAN&<x*<N`N/AN&<x*<N`NC튪NjHANC튰NjL8N C튪NN`:NqAN&<x*<N`NC튪NjAbNN`AbNAbNvNXHAN&<x*<N`&<x*<NBL8N`AbNAbN&<x*< NVJBfNAbN&<x*< N\vNXH <r$<L8N\A퀖NpC튪NjvNXA퀖NN\A퀖NC퀖At 0AZN&<x*<NB&<x*<N\vNX&<x*<N`A퀐NpNpNprNpNܬA퀖N/ <r$<A퀐NN\N"N <r$<A퀖NN\N? <r$<A퀐NN\N? <r$<A퀖NN\N? <r$<AZNN\&<x*<NBA퀐NN`N?A퀖N? <r$<AZNN\&<x*<NBA퀐NN`&<x*<N`N?~NpN~pNpNp NBmX <r$<ANN\ATNVATN&<x*<N`NC튪NjvNXA퀖NN`&<x*<N`A퀖NATN&<x*<N`N/A퀖NC튶NBm <r$<AZNN\ANVAN&<x*<N`N/ATN&<x*<N`NC튞~NvNXA퀖NN\AHNAN&<x*<NBA퀐NN`ANNAN&<x*<N`N/ATN&<x*<N`NCD~NANANzN\JBfN <r$<AHNN\AHNAN&<x*<N`N/ATN&<x*<N`NCJ~NANAHNHANNHANHANHAjN N`VNqN`NqpNpNprNpNܬA퀖N&<x*<N`N/ <r$<A퀐NN\N"NA퀖N&<x*<N`N? <r$<AZNN\&<x*<NBA퀐NN`&<x*<N`N?~NA퀖N&<x*<N`HAN&<x*<N`NC튪NjvNXL8N`A퀖NA퀖N&<x*<N`A큌NpNܬBm <r$<AZNN\ANVAN&<x*<N`NC튰NjvNXA퀖NN\AHNAN&<x*<NBA퀐NN`ANNAN&<x*<N`NCPNjANAN&<x*<N`NCVNjANANzN\JBfN <r$<AHNN\AHNAHNHANNHANHANHAjN N`NqpNܬpNpNA퀖N&<x*<N`N/ <r$<A퀐NN\N"NA퀖N&<x*<N`N? <r$<A퀐NN\N?A퀖N&<x*<N`N? <r$<AZNN\&<x*<NBA퀐NN`N?A퀖N&<x*<N`N? <r$<AZNN\&<x*<NBA퀐NN`&<x*<N`N?~NN NdpN~pNpNp N <hrdNN$Est-ce le 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<r$<L8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fN@Ax 0N NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx 0N Bm|`RN NdAHN TANN TA>N TA> 0AH H0AN 0Bm|AxNzN JBfNNHNvHAHNL8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fN&Ax 0NHNvHAHNL8N\H <r$<L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx 0NHNvHAHNL8N\H <r$<L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNߺAx @0NHNvHAHNL8N\H <r$<L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx 0NHNvHAHNL8N\H <r$<L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNNAx 0NHNvHAHNL8N\H <r$<L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx @0NHNvHAHNL8N\H <r$<L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx `0NHNvHAHNL8N\H <r$< L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx 0`A4N N NdpNܬpNp NprN <P"<^N <P"<N <l"<^N <l"<N <P"<N <P"<N <l"<N <l"<NpNpNprN <P"<^N <l"<^N <P"<N <l"<N <P"<N <l"<N <P"<N <l"<NpN~pNpNp NN$ouilCN> <b"<kNAN>N$nonCN> <b"<NAN>Bm|AxNzN JBfNNHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fN@Ax 0N NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx 0N Bm|`RN NdA8N TA>N TADN TBmNA>N&<x*<NtpJBgp/ <r$<ANN\A>NNtpJBgp$fNN`NvHA퀐NL8N\H <r$<L8N\&<x*<NN&ADNADN&<x*<NtpJBgp/ <r$<AZNN\ADNNtpJBgp$fNNVSgNA8 0A>N&<x*<N`ATNADN&<x*<N`AN`"ANATNNtJBfN pNpNpN <r$<ATNN\&<x*<NBA퀊NN`vNXH <r$<L8N\N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N <r$<ATNN\&<x*<NBA퀊NN`vNX&<x*<N`N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N,pNpNpNpN <r$<ATNN\&<x*<NBA퀊NN`vNXH <r$<L8N\N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N <r$<ATNN\&<x*<NBA퀊NN`vNX&<x*<N`N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N,NpNpNpN <r$<ATNN\&<x*<NBA퀊NN`vNXH <r$<L8N\N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N <r$<ATNN\&<x*<NBA퀊NN`vNX&<x*<N`N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N,pNpNpNpN <r$<ATNN\&<x*<NBA퀊NN`vNXH <r$<L8N\N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N <r$<ATNN\&<x*<NBA퀊NN`vNX&<x*<N`N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N,pN0pNpNpN <T"<N <"<N,A&N N NdC AH 0CJAN 0pN~pNpNp NpNܸAN&<x*<N`ATNNVJBfNAN&<x*<N`NNHPATN&<x*<N`NN"_NCN>N$a =CN>N6AN&<x*<N`NNCN>Nb =CN>AHNvNXH <r$<L8N\ANANNvNXANAN/AN"NAN>pNܸAN&<x*<N`N/AN&<x*<N`N"NAN>AHN&<x*<N`AHNA 0A 0pNܸpN~pNpNp NAN ANATNNtJBfNAN/ATN/ANCD~N8AN/ATN/ANCJ~N8AN/ATN/ANCt~N8AN/ATN/ANCz~N8NxAN/ANCPNAN/ANCVNAN/ANC튀NAN/ANC튆NAhN N NdNDpN~pNpNpNp"<NN$un peu de cours4N>pN~pNpNp NppPr NN$)Li dsignera la Ligne i ,Ci la colonne i. N> <r NN$Ainsi le systme aN> <r2NN$2 x + 3 y - 9 z = 84N> <r2NN$- x + 5 y = 14N> <r2NN$ 3 y - 5 z = 94N> <"<NN$s'crit4N> <"<NN$2 3 -9 84N> <"<NN-1 5 0 1N> <"<NN$0 3 -5 94N>pNܬpNpN?<?<?<|?<?<|?<?<?<~N?<?<?<?<~N?<?<?<&?<?<&?<?<?<~NpNpN <"<:NNL1N> <"<:NNL2N> <"<:NNL3N> <,"<NN C1 C2 C3N>pNpNpN <r$<H <r$<H <r$<H <r$<HAz(N NDpN~pNpNpNprdNN$%oprations sur les lignes et colonnesN>pNpNpNpN~pNpNp Np a Li : multiplier les cofficients et constante de Li par a(non nul)N>pPr NN>Li --> Li + lj : ajouter les lignes Li,Lj (nouvelle ligne Li)N>pdr NN$-Li<-->Lj : change des lignes Li et LjeN>pxr NN$/Ci<-->Cj : change des colonnes Ci et Cj4N>pN~p N <r NN$UN PETIT PLUS !eN>pN~pN <r NNHL'option 'PIVOT H' remplace la suite d'oprations Li --> a Li + b Lj quiN> <r NN.permet de mettre des 0 sous un nombre non nul.N> <r NNHL'option 'PIVOT B' remplace la suite d'oprations Li --> a Li + b Lj quiN> <r NN$5permet de mettre des 0 au-dessus d'un nombre non nul. N>pN~pNpNpN <,r2NN&Ces oprations transforment un systmeN> <Jr2NN$en un systme quivalent.eN>pN~pNpNp NN NdADNAtNAJNAzNAPNAVNA튀NA튆NA튌NA튪NA튞NA튰NAnNA튶NN NdAN <r$<H <r$<H <r$<H <r$<HAz(N AgN N NdpNܸpNpNpNprN <"<N,pNpNpNpr7N <c"<SN,pNpNpNpr2N <h"<NN,pNܸpN~pNpNpNp2rpPrp("<Np2NN>pxrpn"<NpbNN> <"<NN2aN>pNܬ?<?<u?<?<u~Npi"<Np2NN>pn"<,NpNN> <"<'NN4aN> <"<;N <NN>?<)?<u?<=?<u~NN( HPpN"_NHPN = b"_NHP <N"_NHPN - 4ac )"_NCN>px"<NAN>pN~p NpN <r2NN c'est la forme canonique de P(x)N>N$Si HPpN"_NHPN* < 0 , P(x) ne s'annule pour aucune valeur"_NCN>N$Si HPpN"_NHPN* = 0 , P(x) s'annule pour une seule valeur"_NCN>N$Si HPpN"_NHPN$1 > 0 , P(x) s'annule pour exactement deux valeurs4"_NC2N>pN~pNpNpN <r <r <@rN NdpNܸpNpNpNprN <"<N,pNpNpNp$r2N <T"<XN&pNp(r-N <Y"<SN&N$P(x) = a x + b x + cSCN>pNܸpN~pNpNpNpN"<NAN>pN~pNpNp N <T"<NN$A , B ET C SONT RATIONNELS.cN>pN~p@"<6Np2NN> <rdNNAVECN> <"<NN$a =4N>A8NA킲 0Bm <r$<H <r$<H <r$<H <r$<H <r$<H <r$<H <r$<HAnN HxANC튼NHxANC.NpC튼NjzN JBfNhpNpN~px"<N <"<N& <"<NNATTENTION ! LE COEFFICIENT aN> <"<NN$DOIT ETRE NON NULN> <r$<H <r$<H <r$<H <r$<HAz(N A8NNpN~pNpNp N <"<NN$b =4N>A킲 0Bm <r$<H <r$<H <r$<H <r$<H <r$<H <r$<H <r$<HAnN HxANC튼NHxANC.NpN~pNpNp N <"<NN$c =4N>A킲 0Bm <r$<H <r$<H <r$<H <r$<H <r$<H <r$<H <r$<HAnN HxANC튼NHxANC.NA 0 <r$<A NVA N/A NC튼NjCFNA N/A NC.NjCLNN`NqNqN Nd"_ARN "_ALN "_AFN "_A@N "_A:N "_A4N LANN ZLAHN ZHm4Hm:AmN AC4N>AC:N>Hm@HmFAmN AC@N>ACFN>HmLHmRAmN ACLN>ACRN>Hm4p0N"_NJBfN Hm:p1N"_NJBfN^Hm4p1N"_NJBfNJHm4N-1"_NJBfN$N-xCXN>NpxNCXN>AHNHANNHHm4AMN A4NNvvNXAHNN`&<x*<N`AHNHm4AVN ApN&<x*<NVpJBgp/AjNN&AjNNDpJBgp$fND <r$<AHNN\HA4NNvvNXL8N\N/ANN"Np(NN>NXpxNCXN>NpxNCXN>Hm4AtN CAX 0Hm:AtN CA^ 0AHNHANNHHm4Hm:tHtHtHAQAHN&<x*<N`AHNAHN/ANN"NAXN>AHN&<x*<N`A텸NHm4N-1"_NpJBgp/Hm:p1N"_NpJBgp$fN <Ѝ/ <r$< _N pxNCXN>Hm4p0N"_NJBfN *AHN&<x*<N`AHNA@N*HPp-N"_NJBfN Hm@AiN AC@N> <r$<AHNN\N/ANN"Np-NN>N Hm@p0N"_NJBfN  <r$<AHNN\N/ANN"Np+NN>AHN&<x*<N`AHNHm@p0N"_NJBfNzHmFp1N"_NJBfN Hm@p1N"_NJBfN Hm@N-1"_NJBfN N-xCXN>N pxNCXN>AHNHANNHHm@AMN A@NNvvNXAHNN`&<x*<N`AHNHm@AVN ApN&<x*<NDpJBgp/AjNN&AjNNDpJBgp$fN <r$<AHNN\HA@NNvvNXL8N\N/ANN"Np(NN>N pxNCXN>Hm@AtN CAX 0HmFAtN CA^ 0AHNHANNHHm@HmFtHtHtHAQAHN&<x*<N`AHNAHN/ANN"NAXN>AHN&<x*<N`AHNALN.zNDJBfNvALN.zNVJBfNAHN/ANN"Np+NN>N AHN/ANN"Np-NN>ALN.BNCLN>AHN&<x*<N`AHNAHNHANNHHmLHmRtHtHtHAQHm^N ="_NC^N>pN~ <rxNA^N>pN~BmA킲 @0pNܸ <r$<H <r$<H <r$<H <r$<H <r$<HA9N HmHmAmN A탨N/ACNA탨N/ACNHmAVN A탨N/AjNC튼NA탨N/AN.C.NN NdpNܸpNpNpNprN <"<N,pNpNpNp$r2N <T"<XN&pNp(r-N <Y"<SN&pNܸpN~pNpNpNpPrdNN$ L'quation 4N>pN~pNpNp NpNܬpNNx HP <N"_NHPN R ,"_NCN> <"<NAN> <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN AN"<NN$= 0N>pC튼N/pC.NjHpC.NjL8NB _NpC튼N/pC.NjHpC.NjL8NB _NpC튼N/pC.NjHpC.NjL8NB _NpC튼NjANpC튼NjANAN pC튼NjANAN A 0 <r$<A NVA NC튼N/AN _NN`NqNqpC튼Nj&<x*<N6HpC튼NjvNXHpC튼NjL8NBL8N\A텾NA텾N&< x*<NVJBfNHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NNdpN~pNpNp NpNܬA텾NzN\JBfN <rdNNn'admet aucune solution.N>A텾NzN JBfN <rdNN$admet une solution unique , savoirN>pN~pNpNp NpC튼NjBANpC튼NjNPANANNHANNBANANANANzNDJBfN@ANANANANAN <Ѝ/AN _N <Ѝ/AN _NNx' = xHPp"N"_NHPN ="_NCN> <"<NAN> <r$<H <r$<HANHANHAjN A텾NzNVJBfNd <rdNN$admet exactement deux solutions4N>Av 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfNCTAv 0AT 0N`zNqpN~pNpNp NAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fNHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NNdpC튼NjBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튼NjNPNCN>HmHmAmN <"<NNx' =N> <r$<H <r$<HHmHmtHtHtHAQpC튼NjNPNCN>HmHmAmN <"<NNetN>pxNHPp"N"_NHPN ="_NCN> <,"<NAN>HmHmAmN <r$<H <r$<HHmHmtHtHtHAQpN~pNpNp NpNܬpNNx HP <N"_NHPN R ,"_NCN> <"<NAN> <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN AN"<NN$= mN> <rdNNavec m =N>A킲 0pNܸ <r$<H <r$<H <r$<H <r$<H <r$<H <r$<H <r$<HAnN CA 0CA 0pNܸpNpNpNprN <"<N,pNpNpNp$r2N <T"<XN&pNp(r-N <Y"<SN&pN~pNpNpNpPrdNN$ L'quation 4N>pN~pNpNp NpNܬpNNx HP <N"_NHPN R ,"_NCN> <"<NAN> <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN AN"<Np=NN>AN&<x*<N`H <r$<HANNHPANNHPtHtHtHAQA텾NzN JBfN& <rdNN$admet une solution unique , savoirN>pN~pNpNp NpC튼NjBANpC튼NjNPANANNHANNBANANANANzNDJBfN%ANANANANAN <Ѝ/AN _N <Ѝ/AN _NNx' = xHPp"N"_NHPN ="_NCN> <"<NAN> <r$<H <r$<HANHANHAjN A텾NzNVJBfN* <rdNN$admet exactement deux solutions4N>Av 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfN'8CTAv 0AT 0N`zNqpN~pNpNp NAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fN(@HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NN*pC튼NjBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튼NjNPNCN>HmHmAmN <"<NNx' =N> <r$<H <r$<HHmHmtHtHtHAQpC튼NjNPNCN>HmHmAmN <"<NNetN>pxNHPp"N"_NHPN ="_NCN> <,"<NAN>HmHmAmN <r$<H <r$<HHmHmtHtHtHAQpN~pNpNp NpNܬpNNx HP <N"_NHPN R ,"_NCN>pn"<NAN> <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN ANrnNN$> 0N>pC튼N/pC.NjHpC.NjL8NB _NpC튼N/pC.NjHpC.NjL8NB _NpC튼N/pC.NjHpC.NjL8NB _NpC튼NjANpC튼NjANAN pC튼NjANAN A 0 <r$<A NVA NC튼N/AN _NN`NqNqpC튼Nj&<x*<N6HpC튼NjvNXHpC튼NjL8NBL8N\A텾NA텾N&< x*<NVJBfN/ HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NN7pN~pNpNpNpNܬA텾NzN\JBfN/pC튼NjzN\JBfN/N$n'admet aucune solution4CN>N/N"admet R pour ensemble de solutionsCN> <rdNAN>N7A텾NzN JBfN1pC튼NjzN\JBfN0L <rdNN$n'admet aucune solutionON>N1 <rZNN.admet R priv de x0 pour ensemble de solutionsN>pN~pNpNp NpC튼NjBANpC튼NjNPANANNHANNBANANANANzNDJBfN1ANANANANAN <Ѝ/AN _N <Ѝ/AN _N <rdNN$ avec x0 =4N> <r$<H <r$<HANHANHAjN N7pC튼NjzNVJBfN2Nadmet l'ensemble ] -HP <N"_NHPN$ ,x'[ u ] xt"_NHPp"N"_NHPN$ , + 4"_NHP <N"_NHPN ["_NCN>Npour ensemble de solutionsCN>N38N$admet l'intervalle ] x' , xHPp"N"_NHPN [ pour ensemble"_NCN>N de solutionsCN> <rdNAN> <rdNAN>p N <rdNNavecN> <"<NNx' =N> <"r}NNetN>pxNHPp"N"_NHPN ="_NCN> <@"<NAN>Av 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfN4CTAv 0AT 0N`zNqpN~pNpNp NAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fN5HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDN7pC튼NjBHpC튼NjNHL8NBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튼NjNPNCN>HmHmAmN <r$<H <r$<HHmHmtHtHtHAQpC튼NjNPNCN>HmHmAmN <r$<H <r$<HHmHmtHtHtHAQpN~pNpNp NpNܬpNNx HP <N"_NHPN R ,"_NCN>pn"<NAN> <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN ANrnNN$< 0N>pC튼N/pC.NjHpC.NjL8NB _NpC튼N/pC.NjHpC.NjL8NB _NpC튼N/pC.NjHpC.NjL8NB _NpC튼NjANpC튼NjANAN pC튼NjANAN A 0 <r$<A NVA NC튼N/AN _NN`NqNqpC튼Nj&<x*<N6HpC튼NjvNXHpC튼NjL8NBL8N\A텾NA텾N&< x*<NVJBfN;HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NNDpN~pNpNpNpNܬA텾NzN\JBfNN <rdNAN>NDA텾NzN JBfN>pC튼NjzNVJBfN< <rdNN$n'admet aucune solutionON>N> <rZNN.admet R priv de x0 pour ensemble de solutionsN>pN~pNpNp NpC튼NjBANpC튼NjNPANANNHANNBANANANANzNDJBfN>*ANANANANAN <Ѝ/AN _N <Ѝ/AN _N <rdNN$ avec x0 =4N> <r$<H <r$<HANHANHAjN NDpC튼NjzN\JBfN?pNadmet l'ensemble ] -HP <N"_NHPN$ ,x'[ u ] xt"_NHPp"N"_NHPN$ , + 4"_NHP <N"_NHPN ["_NCN>Npour ensemble de solutionsCN>N?N$admet l'intervalle ] x' , xHPp"N"_NHPN [ pour ensemble"_NCN>N de solutionsCN> <rdNAN> <rdNAN>p N <rdNNavecN> <"<NNx' =N> <"r}NNetN>pxNHPp"N"_NHPN ="_NCN> <@"<NAN>Av 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfNApCTAv 0AT 0N`zNqpN~pNpNp NAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fNBxHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NNDpC튼NjBHpC튼NjNHL8NBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튼NjNPNCN>HmHmAmN <r$<H <r$<HHmHmtHtHtHAQpC튼NjNPNCN>HmHmAmN <r$<H <r$<HHmHmtHtHtHAQpN~pNpNp NpNܬpNNx HP <N"_NHPN R ,"_NCN>pn"<NAN> <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN <NHPN 0"_NCN>ANrnNAN>pC튼N/pC.NjHpC.NjL8NB _NpC튼N/pC.NjHpC.NjL8NB _NpC튼N/pC.NjHpC.NjL8NB _NpC튼NjANpC튼NjANAN pC튼NjANAN A 0 <r$<A NVA NC튼N/AN _NN`NqNqpC튼Nj&<x*<N6HpC튼NjvNXHpC튼NjL8NBL8N\A텾NA텾N&< x*<NVJBfNHHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NNQtpN~pNpNpNpNܬA텾NzN\JBfNItpC튼NjzN\JBfNI*N$n'admet aucune solution4CN>NIZN"admet R pour ensemble de solutionsCN> <rdNAN>NQtA텾NzN JBfNKvpC튼NjzN\JBfNK8 <rdNN$admet une unique solution ,x0N>pN~pNpNp NpC튼NjBANpC튼NjNPANANNHANNBANANANANzNDJBfNJANANANANAN <Ѝ/AN _N <Ѝ/AN _N <rdNN$ avec x0 =4N> <r$<H <r$<HANHANHAjN NKp <rdNN"admet R pour ensemble de solutionsN>NQtpC튼NjzNVJBfNLPNadmet l'ensemble ] -HP <N"_NHPN$ ,x'] u [ x4"_NHPp"N"_NHPN$ , + 4"_NHP <N"_NHPN ["_NCN>Npour ensemble de solutionsCN>NLN$admet l'intervalle [ x' , xHPp"N"_NHPN ] pour ensemble"_NCN>N de solutionsCN> <rdNAN> <rdNAN>p N <rdNNavecN> <"<NNx' =N> <"r}NNetN>pxNHPp"N"_NHPN ="_NCN> <@"<NAN>Av 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfNNPCTAv 0AT 0N`zNqpN~pNpNp NAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fNOXHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NNQtpC튼NjBHpC튼NjNHL8NBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튼NjNPNCN>HmHmAmN <r$<H <r$<HHmHmtHtHtHAQpC튼NjNPNCN>HmHmAmN <r$<H <r$<HHmHmtHtHtHAQpN~pNpNp NpNܬpNNx HP <N"_NHPN R ,"_NCN>pn"<NAN> <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN <NHPN 0"_NCN>ANrnNAN>pC튼N/pC.NjHpC.NjL8NB _NpC튼N/pC.NjHpC.NjL8NB _NpC튼N/pC.NjHpC.NjL8NB _NpC튼NjANpC튼NjANAN pC튼NjANAN A 0 <r$<A NVA NC튼N/AN _NN`NqNqpC튼Nj&<x*<N6HpC튼NjvNXHpC튼NjL8NBL8N\A텾NA텾N&< x*<NVJBfNUHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NN^TpN~pNpNpNpNܬA텾NzN\JBfNVTpC튼NjzNVJBfNV N$n'admet aucune solution4CN>NV:N"admet R pour ensemble de solutionsCN> <rdNAN>N^TA텾NzN JBfNXVpC튼NjzNVJBfNX <rdNN$admet une unique solution ,x0N>pN~pNpNp NpC튼NjBANpC튼NjNPANANNHANNBANANANANzNDJBfNWANANANANAN <Ѝ/AN _N <Ѝ/AN _N <rdNN$ avec x0 =4N> <r$<H <r$<HANHANHAjN NXP <rdNN"admet R pour ensemble de solutionsN>N^TpC튼NjzN\JBfNY0Nadmet l'ensemble ] -HP <N"_NHPN$ ,x'] u [ x4"_NHPp"N"_NHPN$ , + 4"_NHP <N"_NHPN ["_NCN>Npour ensemble de solutionsCN>NYN$admet l'intervalle [ x' , xHPp"N"_NHPN ] pour ensemble"_NCN>N de solutionsCN> <rdNAN> <rdNAN>p N <rdNNavecN> <"<NNx' =N> <"r}NNetN>pxNHPp"N"_NHPN ="_NCN> <@"<NAN>Av 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfN[0CTAv 0AT 0N`zNqpN~pNpNp NAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fN\8HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NN^TpC튼NjBHpC튼NjNHL8NBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튼NjNPNCN>HmHmAmN <r$<H <r$<HHmHmtHtHtHAQpC튼NjNPNCN>HmHmAmN <r$<H <r$<HHmHmtHtHtHAQN_nN Le maximum du polynome suivant :CN>pZrdNAN>pN~pNpNp NpNܬpN <"<NNP(x) =N> <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN <rdNN est atteint pour la valeurN>pC튼NjBHpC.NjL8NBNHPpC.NjNPHpC튼NjL8NBNHPAmN <r$<H <r$<HHmHmtHtHtHAQAN.A텲NACN>pC.NjHpC.NjL8NBHpC.NjL8NBA텲NNBA텲NNBNCN>HmHmAjvN A텎N&<x*<N JBfNbrHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NBmNgA퇞CN>HmpC튼NjHpC.NjL8NBHpC.NjL8NBNHPAjvN A텎N&<x*<N JBfNcfHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NBmNgA퇞CN>HmpC튼NjHpC.NjL8NBHpC.NjL8NBA텲NNBNHPAjvN A텎N&<x*<N JBfNdfHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NBmNgHmHmAgN A텎N&<x*<N JBfNeHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NBmNgAzCN>HmpC튼NjHpC.NjL8NBHpC.NjL8NBA텲NNBA텲NNBNHPAgN A텎N&<x*<N JBfNf"HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NBmNgAzCN>HmHmAmN A텎N&<x*<N JBfNfHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NBmNgACN>ACN>HmAVN pNܬ <r$<H <r$<HHmHmtHtHtHAQ <T"<NAN>N NdpNpNpNpNpNpNܸprN <"<N,pNpNpNpr7N <c"<SN,pNpNpNpr2N <h"<NN,pNܸpN~pNpNpNpNܸN$ Soit (E) : x HP <N"_NHPN( R , a x + b x + c = 0 ( a non nul )"_NCN>p2rp("< Np2NN>pNHPN$ = b - 4 a c4"_NCN>pPrpKrlNp2NN>N 1er cas : HPpN"_NHPN < 0"_NCN>pN~pNpdrpNpxr2NN$(E) n'admet aucune solution N>N$ 2me cas : HPpN"_NHPN = 0"_NCN>pN <rpN <r2NN$(E) n'admet qu'une solution4N>Nx' = xHPp"N"_NHPN = -"_NCN> <r <"<NpbNN> <"<NN2aN>pNܬ?<?<?<?<~NN$ 3me cas : HPpN"_NHPN > 0"_NCN>pN <rpN <r2NN(E) admet pour solutionsN> <@rN-b - HPpN"_NCN> <6rdNAN>?<?<1?<?<6?<?<,?<?<,~N <Jr}NN2aN>?<d?< <@"<NAN>N-b + HPpN"_NCN> <6"<NAN>?<?<1?< ?<6?<?<,?<?<,~N <J"<NN2aN>?<?<pN~pN <"<8NN-N'utilisez les formules queN> <"<@NN$quand elles s'imposent.4N> <"<8NN$-Pensez aux racines videntes4N> <"<8NN$-La forme canonique est4N> <"<@NN$parfois intressante.4N> <,"<8NN-Les formules rduites aussiN>N NdpNܸpNpNpNprN <"<N,pNpNpNp$r2N <T"<XN&pNp(r-N <Y"<SN&pC튼NjNpNܬp N <"<NNP(x) =N> <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN pN~ <rxNNn'est pas factorisable dans R.N>A텚NzN JBfN|pC튼NjHpC.NjL8N JBfNtpC튼NjzN JBfNqpN~pNpNp@N <"<NNHUMOUR !N>NtpN~pNpNpNpxrxNNFactorisation de :N>pN~p N <"<NNP(x) =N>pNܬ <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN pN~pNܬpC튼NjHpC튼NjL8NBzN\JBfNs N P(x) = ( x -CN>Ns&N P(x) = ( x +CN> <"<NAN>pC튼NjHpC.NjL8NBNHPpC튼NjNPHpC.NjL8NBNHPAmN <r$<H <r$<HAN.HAN.HAjN HmAtN CA 0HmAtN ANANN ANAN&<x*<N`N"<Np)NN>AN&<x*<N`N"<Np2NN>N|pC튼NjzN JBfNtpN~pNpNp@N <"<NNHUMOUR !N>N|pN~pNpNpNpxrxNNFactorisation de :N>pN~p N <"<NNP(x) =N>pNܬ <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN pN~pNܬpC튼NjzNVpJBgp/pC튼NjHpC.NjL8N`zNDpJBgp$fNy <"<NNP(x) =N> <r$<H <r$<HpC튼NjHpC.NjHAjN pC튼NjNNNvHpC.NjNNNvL8N vNXANAN&<x*<N`AHNpC튼NjzN\JBfNwP NwN$( x +CN>pC튼N/pC.Nj _NpC.N/pC튼Nj _NpC튼N/pC.Nj _NpC.N/pC튼Nj _NHx <r$<C튼NHx <r$<C.NAHN"<NAN>pC튼NjNHPpC.NjNPNHPAmN AHN&<x*<N`H <r$<HAN.HAN.HAjN HmAtN CA 0HmAtN ANANN AN AHN&<x*<N`ANN`N"<Np2NN>N|pC튼NjHpC.NjBL8N JBfN|pN~pNpNpNpxrxNNFactorisation de :N>pN~p N <"<NNP(x) =N>pNܬ <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN pN~pNܬpC튼NjHpC튼NjL8NBzN\JBfN{NNP(x) = - ( x -CN>N{jNP(x) = - ( x +CN> <"<NAN>pC튼NjHpC.NjL8NBNHPpC튼NjHpC.NjL8NBNPNHPAmN  <r$<H <r$<HAN.HAN.HAjN HmAtN CA 0HmAtN ANANN ANAN&<x*<N`N"<Np)NN>AN&<x*<N`N"<Np2NN>A텚NzNVJBfNpNܸpC튼NjzN JBfN~pN~pNpxrxNN$'Soit factoriser le polynome suivant :GN>pNܬp N <"<NNP(x) =N> <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN pN~pN~p N <rnNN$Il n'y a ici aucune difficult.N> <rnNN&Il vous suffit de mettre x en facteur.N>NpN~pNpNpNpxrxNNFactorisation de :N>pN~p N <"<NNP(x) =N>pNܬ <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN pN~pNܬpC튼Nj&<x*<N6HpC.Nj&<x*<N6L8N JBfNpC튼NjHpC.NjL8N JBfN@N P(x) = ( xCN>AH 00NpC튼NjHpC.NjL8N`zN JBfNN P(x) = - ( xCN>AH T0pN~p N <rxNAN>AHN&<x*<N`AHNN> <rxNNP(x) =N> <r$<H <r$<HpC튼NjHpC.NjHAjN pC튼NjNNNvHpC.NjNNNvL8N vNXANAN&<x*<N`AHNpC튼NjzN\JBfN AHN&<x*<N`AHNpC튼N/pC.NjHpC.NjL8NB _NpC튼N/pC.NjHpC.NjL8NB _NpC튼N/pC.NjHpC.NjL8NB _NpC튼NjANpC튼NjANAN pC튼NjANAN A 0 <r$<A NVA NC튼N/AN _NN`NqNqpC튼Nj&<x*<N6HpC튼NjvNXHpC튼NjL8NBL8N\A텾NA텾N&< x*<NVJBfNhHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrpr.NXHx. <r$<C틎NNDNpN~pNpNpNpNܬAv 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfNTCTAv 0AT 0N`zNqpN~pNpNp NAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fN\HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틎NN7pC튼NjBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튼NjNPNCN>HmHmAmN NAHN"<Np+NN>AHN&<x*<N`AHNAHNH <r$<HAjNHAN.HAjN ANNvHANNvL8N vNXAHNN`&<x*<N`AHNAHN"<NN$) ( xN>AHN&<x*<N`AHNpC튼NjBNHPp+N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튼NjNPNCN>HmHmAmN HmAVN AjNzNVJBfNAHN"<Np-NN>NAHN"<Np+NN>AHN&<x*<N`AHNAHNH <r$<HAjNHAN.HAjN ANNvHANNvL8N vNXAHNN`&<x*<N`AHNAHN"<Np)NN>NAN*HPp-N"_NJBfNAHN"<Np-NN>AC>N>NHmp"_NC>N>AHN"<Np+NN> HmtHtHtHAQAtN pC튼NjNPNCN>HmHmAmN AN*HPp-N"_NJBfNAHN"<Np-NN>AC>N>NHmp"_NC>N>AHN"<Np+NN> HmtHtHtHAQAtN N NdpNܸpNpNpNprN <"<N,pNpNpNp$r2N <T"<XN&pNp(r-N <Y"<SN&pN~pNpNpN <rdNNSoit le polynome suivant :N>pN~p NpNܬpN <"<NNP(x) =N> <r$<H <r$<HpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPpC튼NjNHPpC.NjNHPAN N NdpNA*N AN N NdLAN ZLA킈N ZLA킲N ZLA킬N ZLAN ZLANN ZLAHN ZpNܸN\A킲NNpNprNA킲NNܬA킲NN~pNpNp NA킬NNA킈NNANNCHA 0CNA 0AN CHA 0CNA 0A8NA킲NNܬNCN>HmA "_NJBgNCN>Hmp N"_NpJBgp/AN*HPp0N"_NpJBgp/AN.zN pJBgp$fN@A CN>A8NAN CHA 0CNA 0ANHPpAN"_NpJBgp/HmpN"_NpJBgp$fNA8NAN CHA 0CNA 0Hmp-N"_NJBfNHmA "_NJBfNp-NCN>AN/AN"Np-NN>Hmp N"_NpJBgp/Hmp/N"_NpJBgp$fNnANzN JBfNnAN.zNDJBfNnA8NA 0ANNvvNXANN`ANAN/ <r$<ANN\N"NAN&<x*<N`N/ <r$<ANN\N"N <r$<ANN\ANAN/AN"NAN>Hmp0N"_N pJBgp/Hmp9N"_N pJBgp$fNAN/AN"NAN>NAN&<x*<N`ANAN/ <r$<ANN\N"NANNvHANNvL8N vNXANN`&<x*<N`N/ <r$<ANN\N"NAN/AN"NAN>Hmp N"_NJBgPAN.zN JBfNxp1NCN>AN.ANAN.ANAN AN.ANNANAN.ANNANANANN&<x*<NVpJBgp/HmA "_NpJBgp/Hmp-N"_NpJBgp$fNA8NAN CHA 0CNA 0NvA8NANHANHANHANHAjN NzN NdA n0A n0NzpNܸpNpNpNprN <"<N,pNpNpNp$r2N <T"<XN&pNp(r-N <Y"<SN&pNܸpN~p NpNpNppN~pNpNpNpPr2NN$A1 - Vous avez la possibilit d'introduire un polynome de degr au4N>pdr2NN$ plus gal 8dN>pxr2NN$C2 - La mthode retenue pour le calcul de P(a) , a rel quelconque ,4N> <r2NN: est la la mthode de HORNER qui est TRS PERFORMANTE .N> <r2NN@ Pour un calcul approch , choisir l'option 'donne dcimale'N> <r2NN$; Pour une rponse exacte , choisir l'option ' autre '4N>pN~pNpNpN <"<NNExemple : P(x) = xN>pN~pNpNp N <"<rN <r$<NN> <Jr2NN$ a = 1.4144N>pNܬpNpNprN?<?<?<:?<?<:?<E~NpNpNprN?<:?<E?<?<E~NpNpNprN <,r2NN$a =4N> <r$<H <r$<HNR2HPAMN pNpN?<?<?<?<?<?<'~NpNpNprN?<?<'?<?<'~NpNpNprNpNpN~pNܬ <^rN <rrN, <^rN <rrN <nrNpNN>NVJfNV/NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp$gppNܸpNpNpNprN <"<N,pNpNpNp$r2N <T"<XN&pNp(r-N <Y"<SN&pN~p NpNpNppN~pNpNpNpPr2NN>- Il n'existe pas de formules pour la rsolution des quationsN>pdr2NN$= P(x) = 0 , P tant un polynome de degr au moins gal 5 .4N> <r2NN$A- C' est donc vous d'imposer vos contraintes sur P(x) et sur la4N> <r2NN0 distance entre les ventuelles racines de P(x)N> <r2NNP(x) = 0 <==> | P(x) | < eN> <"<@NN$!Distance minimale entre 2 racines(N> <r$<H <r$<HNe = 0.01HPA$N <r$<H <r$<HN$ e = 0.001HPA$N <r$<H <r$<HN e = 0.000001HPA$N <r$<H <r$<HN$0.1 HPA$N <r$<H <r$<HN$0.001HPA$N <r$<H <r$<HN$0.00001HPA$N pN~ <"<NpNN> <"<|NpNN> <r$<H <r$<H <r$<H <r$<HN$O KiHPA|N pN~pNpNp N <r"<NN$+L'algorithme de recherche est la DICHOTOMIE4N>NVJfpNNHNvH <r$<L8N\&<x*<N\JBfNjN`NvH <r$<L8N\&<x*<N\JBfN.NV$fN.pN <"<N <J"<N, <"<NpNN>A # =0qN`NvH <r$<L8N\&<x*<N\JBfNNV$fNpN <"<N <J"<N, <"<NpNN>A n0N`NvH <r$<L8N\&<x*<N\JBfNjNV$fNjpN <"<N <J"<N, <@"<NpNN>A 'ŬG0NHNvH <r$<L8N\&<x*<N\JBfNN`NvH <r$<L8N\&<x*<N\JBfNJNV$fNJpN <"<|N <J"<N, <"<|NpNN>A L0N`NvH <r$<L8N\&<x*<N\JBfNNV$fNpN <"<|N <J"<N, <"<|NpNN>A n0N`NvH <r$<L8N\&<x*<N\JBfNNV$fNpN <"<|N <J"<N, <@"<|NpNN>A 'ŬG0NV/NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp$g8NDN Nd"_A8N LANN ZLAHN ZpNܸpNpNpNpN~pNܬAHN/ANN"NAHN&<x*<N`N/ANN&<x*<N`N"N,AHN&<x*<N`N/ANN&<x*<N`N"NAHN&<x*<N`N/ANN&<x*<N`N"NAHN&<x*<N`HA8NNvvNXL8N\N/ANN&<x*<N`N"NA8N>N NdNzA$ 0AN AN AN TAN TNDAN pNpNpNpNpNpr2N <r7N,pr2Np"<N, <r2N <"<N,p"<N <"<N,A$ 0 <r$<A$NV <r$<A$NN\&<x*<NB&<x*<N`ANNA 0 <r$<A NVA$NA NNB&<x*<N JBfNPp1NCN>N^pxNCN> <r$<A NN\&<x*<NB&<x*<N`AHNAHNHANNH <r$<H <r$<HtHHmAXN ANAN&<x*<NVJBfNpN~pNpNpNAHN&<x*<N`N/ANN&<x*<N`N"N <r$<ANN\NN>N`hNqN`Nq?<2?<?<9?<A(" NpN~pNpNpNpNܬp,"<@NpF"<Np@"<TNN valider P(x)N>ph"<@N <"<Np|"<TNN annuler P(x)N>A CN>NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp/NV$fNZpNܸph"<@N <"<N,p Nph"<@N <"<N,pNܸAN NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp/NV$fNNNHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp$fNNHNvH <r$<L8N\&<x*<NN&&<x*<N`A NN`NvH <r$<L8N\&<x*<NN&&<x*<N`A$NA6NA NNDpJBgp/ABNA$NNDpJBgp$fN?<2?<A("N"pNܸ <r$<A NN\&<x*<NB&<x*<N`N/ <r$<A$NN\&<x*<NB&<x*<N`N"N <r$<A NN\&<x*<NB&<x*<N`N/ <r$<A$NN\&<x*<NB&<x*<N`N"N,pNܸC A6 0C$AB 0NV$fNBmA N&<x*<NVpJBgp/A$N&<x*<NVpJBgp$fNNle cofficient de x :CN> <r$<A$NN\&<x*<NBA NN`H <r$<L8N\ANAH C0N(N$le terme constant :CN>AH 90pN~pNpNpNN$ Indiquez HPA"_NCN> <r2NAN>AN gNAN&<x*<NVJBfN <"<^NANNN>pN~pNpNp NA킲 0BmAHNH <r$<H <r$<H <r$<H <r$<HA9N AC>N>ACVN>HmAWN ACN>HmAWN ACN>HmHmAmN HmAVN AN/AjNC튼NHmAVN AN/AjNC.NHmAtN CA& 0HmAtN A&NANN &<x*<NtJBfNAN/A>CNAN/AVCNNAN/ACNAN/ACNNzA 0pN <rN <"<N, <r$<HArN NFA6NzNDJBfNF?<2?<A("N"Bm:BmFANJBgHmN$valider"_NJBgpNܸpNp,"<@NpF"<N,pNp,"<@NpF"<N,pNܸA C(N>pNprN <"<N, <r$<H <r$<HtHA"N pN~AN&<x*< NVJBfNd <r$<HArN NPpNpNpNprN <"<N,pN~pNpNpNpdrdNNSOIT LE POLYNOME SUIVANT :N>ANvNX&<x*<N\H <r$<L8N\AHNpN <r$<AHNN\N"<NAHN&<@x*< N\N"<N(pNܬ <r$<AHNN\N"<NAHN&<x*< N\N"<N"pN~pNpNp N <r$<AHNN\N"<NNP(x) =N>AHN&<x*<N`H <r$<HtHA"N N Nd"_AN LATN ZLANN ZLAHN ZLANN ZLAHN ZpNܸAHNNpNANNNAHN/ANN"NAHN&<x*<N`N/ANN&<x*<N`N"N,pNܸATNN~pNpNp NAHN&<x*<N`HANNvvNXL8N\N/ANN&<x*<N`N"NAN>N NdA N TA CN>BmBmBm <r$<A NVA N/p0NCNA N/p1NCNN`NqNqtA튼N8 <r$<A.N8tAjN8 <r$<HArN N NdLANN ZA N TA&N TpNpNpN~pNpNp NpNܬpNANNrNANN&<x*<N`N"<{N,ANNrNANN&<x*<N`N"<{N <r$<ANNN\N"<DNNconst.N> <r$<ANNN\N"<NpxNN>Bm <r$<A NVA N&<x*<NB&<x*<N`&<x*<N`N/ <r$<ANNN\N"NpxNN>pN~pNpNpNA N&<x*<NB&<x*<N`&<x*<N`N/ <r$<ANNN\N"NA N&<x*<N\NN>pN~pNpNp NN`NqpN~A 0tA NVA N&<x*<NB&<x*<N`N?ANN?A N&<x*<NB&<x*<N`N?ANN&<x*<N`N?~NA NCNHPp0N"_NJBfNA NCNHPAtN CA& 0A NCNHPAtN A N&<x*<N\&<x*<NB&<x*<N`&<x*<N`HA&NANN vNXL8N\AHNA N/A&NANN CjNAHNHANN&<x*<N`HA NCNHPA NCNHPtHtHtHAQNAHN/ANN"NN$+ 1N> N.AHN/ANN"NN$- xN> NANJBfN¨AHN/ANN"Np+NN> AHNHANNHHmAMN A NCNHPAiN ACN> AHNHANNHHmA NCNHPtHtHtHAQ ApN&<x*<NVpJBgp/pCNHPp0N"_NpJBgp$fNNxpCNHPAtN CA 0pCNHPAtN pN~pNpNp N <"<NN$P(x) = 4N> <r$<H <r$<H <r$<HA"N NNpN~pNpNpNN(mthode de HORNER pour le calcul de P(a)CN>p(rdNAN>pN~pNpNp NAN&<x*<N`&<x*<NB&<x*<N\AtNAN&<x*<N`&<x*<NBAtNN`ANpNܬAtNrdNAN"<NA 0AN&<x*<N`A NVA N&<x*<NBAtNN`N??<dA N&<x*<NBAtNN`N??<~NN`NqNqAtN??<AN??<~NCA 0tA NVAtN&<x*<N`HA NANN\&<x*<NBL8N`AHNA NzN JBfN <r$<AHNN\NrZNNconst.N>NAHNrZNpxNN>A N&<x*<NVJBfNpN~pNpNpNAHN&<x*<N`NrPNA NNN>pN~pNpNp N <T"<N <r"<N <h"<,NN$autre4N>NVJfNHNvH <r$<L8N\&<x*<N\JBfNHN`NvH <r$<L8N\&<x*<N\JBfNҸNV$fNҲpNܸ <,"<N <J"<N,p NpNܸAx 0NHN`NvH <r$<L8N\&<x*<N\JBfNHNV$fNHpNܸ <T"<N <r"<N,p NpNܸAx 0AxNJBgpN <,"<N <r"<N,BmAtN"<TNN$a =4N>AxN&<x*<N JBfN`A킲 0pNܬAtN&<x*<N`H <r$<H <r$<H <r$<H <r$<HA9N AC4N>AC:N>Hm4Hm:AmN AC4N>AC:N>Hm4AtN CAH 0Hm:AtN AHNANN AHNAtN&<x*<N`N"<,N <h"<N,AtN&<x*<N`H <r$<HHm4Hm:tHtHtHAQN8ANNC2N> AHN"<NA2N> <Ѝ/ <r$<A NN\NC튼NjH <r$<A NN\NC.NjL8N _NAtN&<x*<N`HA NANN\&<x*<N`&<x*<NBL8N`AHNANNNQlNANNHPp"_NPHPp*N"_NC2N>NANNC2N> N`~NqAtN"<@NAtN&<x*<N`N"<^N.AtN"<TNNP ( HPAjNN"_NHPN ) ="_NN>pN~pNpNpNAtN&<x*<N`HAjNNNNvvNXL8N`N"<TNANNN>pN~pNpNp NNANCNCN>ANCNCN>CA 0 <r$<A NVHmHm4AjvN A텎N&<x*<N JBfNXA 0HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLES4HPN OK r"_ NAvNrNA퇞CN>HmHm:AjvN A텎N&<x*<N JBfNA 0HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNA퇞C N>AtN&<x*<N`HA NANN\&<x*<N`&<x*<NBL8N`AHNpNܬpNpNprN <r$<AHNN\N??< <r$<AHNN\N??<~NpNpNprNpNܬ <r$<HAN <r$<A NN\NCNHPHmAjvN A텎N&<x*<N JBfNA 0HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLES4HPN OK r"_ NAvNrNA퇞CN> <r$<A NN\NCNHPHmAjvN A텎N&<x*<N JBfN߄A 0HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNA퇞C N>HmHm AgN A텎N&<x*<N JBfN$A 0HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNAzCN> <r$<A NN\NCNHPHmAjvN A텎N&<x*<N JBfNA 0HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNA퇞C N>AtN&<x*<N`HA NANN\&<x*<N`&<x*<NBL8N`N"<Np+NN> <r$<HAN N`8NqA텎N&<x*<N JBfNN <,rN <"<N, <Tr NNP(N> <r$<H <r$<HHm4Hm:tHtHtHAQpN~A킲 0pNܬAHN&<x*<N`H <r$<HHmHmtHtHtHAQ <T"<N <v"<vNBmA C,N>N NdLANN ZANN TATN TAZN THmAWN A텎N&<x*<N JBfN,NACN>Hm AWN A텎N&<x*<N JBfNpNAC N>HmAtN CAN 0Hm AtN CAT 0HmHm AmN A텎N&<x*<N JBfNNACN>ACN>HmAtN ANNvvNXANN AZNAZN&<x*<NtJBfN8ATNANNN &<x*<NtJBfNjHmAVN AtN&<x*<N`HA NANN\&<x*<N`&<x*<NBL8N`AHNAHN/ANN"NA2N>N2AtN&<x*<N`HATNANNN vNXL8N\HA NANN\&<x*<N`&<x*<NBL8N`AHNAHNHANNHHmHm tHtHtHAQpN~AN&<x*< NVJBfNh <r$<HArN N: <r$<ANN\vNX&<x*<N\AHNpN~pNpNp N <r$<AHNN\NrdNNP(x) =N>AHN&<x*<N`H <r$<H <r$<HA"N NzANzNVJBfNpN <r2N <@"<N,pNܬpNpN <r4N <>"< NpN~pNpNp N <rFNN$intervalle de recherche4N> <rpN~ <"<NN( |a-b| < 20 )N>pN <"<rN <@"<NN,pNܬ <"<tN <>"<LNpN~ <"<NN$ visualisation4N> <"<N <"<NpN~ <"<NN$oui4N> <"<N <,"<N <""<NN$non4N>?<r?<?<N?<@A&" NpNNV$fNN`NvH <r$<L8N\&<x*<N\JBfNNHNvH <r$<L8N\&<x*<N\JBfN@pN <rZN <6"<N, <rPN <6"<N,AZN A` 0NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp$fN ?<r?<A&"N"pNܸ <"<N <"<N,pNܸAf 0pNNHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp$fN?<r?<A&"N"pNܸ <"<N <,"<N,pNܸAf 0pNA`N/AfNzNDpJBgp$g2A C&N>AfN&<x*<N JBfN~pN <r2N <@"<N,pNܬpNpN <r4N <>"< NpN~ <rdNN$limites de P(x)4N>pN~ <rFN <"<N <rxNN [ -1 , 1 ]N> <rFN <"<N < rdNN[ -0.1 , 0.1 ]N> <rFN <4"<N <.r_NN[ -0.01 , 0.01 ]N>NV/NHNvH <r$<L8N\&<x*<N\pJBgp$fNdN`NvH <r$<L8N\&<x*<N\JBfNhAx 0pNܸ <rFN <"<N,pNpNܸN`NvH <r$<L8N\&<x*<N\JBfNAx L0pNܸ <rFN <"<N,pNpNܸN`NvH <r$<L8N\&<x*<N\JBfNdAx # =0qpNܸ <rFN <4"<N,pNpNܸAxNzNDJBg"pNprN <"<N,pNpNܬp <,rNp-NHPAxNN"_NN> <rNN$ 0N> <@r2NNx = HPA킦NN"_NN> <@"<DNANNN>Bg?<D?<?<^A8" NA$ 0 <r$<&<x*<A$NBgA$N?A8"N"N`NqNqA C8N> <r$<HAtN NN\pN <r2N <T"<NN,pNܬ <r <rPNN<1 - Recherche des intervalles sur lesquels P est strictementN> <rPNN monotoneN> <rPNN$2 - Utilisation du thorme :sN> <rPNN> f tant une fonction drivable et strictement monotone surN> <,rPNN$= [ a , b ] , si f(a)f(b) < 0 il existe une unique solution4N> <;rPNN$' sur ] a , b [ l'quation f(x) = 0eN> <JrPNN43 - Recherche des ventuelles racines par DICHOTOMIEN> <r$<HAtN A$NzNVJBfNpN~pNpNp NN$Sur l'intervalle [ nHPA킦NN"_NHPN$ , 4"_NHPANN"_NHPN$ ] , 4"_NCN>A$N&<x*<N JBfN Nje ne trouve qu'une racine .CN>NNN je trouve HPA$NN"_NHPN racines ."_NCN>A톢N&<x*<N`NrNzNNpN~pNpNpNpC튼NjzN JBfN <r2NN$-Tout rel est solution de l'quation P(x) = 0N>NN <r2NN.Il n'y a aucune solution l'quation P(x) = 0N>NzN Nd <rPNN$a = N>A킬 0N\ <r$<H <r$<H <r$<H <r$< H <r$< HAuVN CjA킦 0 <,rPNN$b =N> <r$<H <r$<H <r$<H <r$<A킦NN\HA킦N&<x*<N`HAuVN CjA 0pNA킦NANNN|JBfN <rnN <6"<N,NA킦NANNVJBfNhAC킦  "002 <rnN <6"<N, <rnNA킦NNN> <,rnNANNN>NzN NdLANN ZpN~pNpNpNANN"<NN(RECHERCHE L'AIDE DE VOS CONTRAINTES...N>pN~pNpNp NBmXBm(BA킦NC틈NAN TA N T`NLAHN ZpC튼NjHpC.NjL8NHAHN&<x*<N6L8NBHpC튼NjHpC.NjL8NHAHN&<x*<N6L8NBL8N`HpC튼NjHpC.NjL8NHAHN&<x*<N6L8NBL8N`HpC튼NjHpC.NjL8NHAHN&<x*<N6L8NBL8N`N `LAHN ZAHNHA"N HpC튼NjHpC.NjL8NHAHN&<x*<N6L8NBL8N`HpC튼NjHpC.NjL8NHAHN&<x*<N6L8NBL8N`HpC튼NjHpC.NjL8NHAHN&<x*<N6L8NBL8N`HpC튼NjHpC.NjL8NAHNNBL8N`HpC튼NjHpC.NjL8NL8N`N `LAHN ZpC튼NjvNXHpC.NjL8NHAHN&<x*<N6L8NBHpC튼Nj&<x*<NBHpC.NjL8NHAHN&<x*<N6L8NBL8N`HpC튼Nj&<x*<NBHpC.NjL8NHAHN&<x*<N6L8NBL8N`HpC튼Nj&<x*<NBHpC.NjL8NHAHN&<x*<N6L8NBL8N`N `LLAHN ZAHNHAN HpC튼NjvNXHpC.NjL8NHAHN&<x*<N6L8NBL8N`HpC튼Nj&<x*<NBHpC.NjL8NHAHN&<x*<N6L8NBL8N`HpC튼NjNPHpC.NjL8NAHNNBL8N`HpC튼NjHpC.NjL8NL8N`N CA 0AN&<n8<*<NVJBfN A n0C킦AH 0AHNHAN ArNArNzN JBfN pN~pNpNp NAN/ANN&<x*<N`N"NND - Un conseil : travailler avec un intervalle sur lequel la fonctionN>AN/ANN&<x*<N`N"NN,  P est strictement monotone .N>AN/ANN&<x*<N`N"NN, ( Elle est drivable sur R )N>N NdLA톖N ZLA N ZLAN ZLA톐N ZANHArN A킈NA NHArN ANA킈NANN\JBfN BmANA킈NNBzNzJBfNCA 0C A 0ANHArN zN pJBgp/A킈NzN pJBgp$fN CAH 0NN ANHArN zN JBfN CAH 0NANANN`vNXAHNAHNHArN A탴NA탴NzN JBfNBNANHArN ANANA탴NNBzN\JBfNCHA 0NCHA 0ANANN\&<8<*<NVJBfNN A톖NAHNN\ANN\JBfNNCHA 0A$NvNXHA$NvNXN&L8N JBfNA톜 p0A$N&<x*<NBANNN`A톢NNA톜 /0A$NzN JBfNA$NzN pJBgp/AfN&<x*<N pJBgp$fN$pN <rA톜N/A톢N"NHmXAHNN"_NN>A$NpNpNprNpNܬpNܸAfN&<x*<N JBfNvA톐N&<x*<N JBfNA킦NAHNN\A톄NNB&<x*<NB&<x*<N`N??<A킦NAHNN\A톄NNB&<x*<NB&<x*<N`N??<~NNvA킦NAHNN\A톄NNB&<x*<NB&<x*<N`N??<A킦NAHNN\A톄NNB&<x*<NB&<x*<N`N??<~NpNpNprNpNܸp NN Ndpp@pWBg?<NN\pp@pW?<?<NN\pp@pW?<?<NN\pp@pW?<?<NN\A톴 @0N NdA%N ANHA!N N NdAN TAN TAN&<x*<N JBfNAN&<x*<N6HA킦NvNXA"NNBL8N\A텚NA텚NBHA킦NvNXL8NANAN&<8<*<NBANNBANN\N&ANA8NN\pNܬpNN`ANrpNpNprNBgAN??<AN?~NANANN\HAN&<8<*<NBL8NANNm HP <N"_NHPp N"_NHPANN"_NCN> <r$<ANN\Nr NAN>pNܬp NAN&<x*<N6HA킦NvNXHANA"NN\L8NBL8N\A텚NpNpNprNANANN\zN JBfNANBHA킦NNPL8NANpNNx' = xHPp"N"_NHPp N"_NHP <N"_NHPp N"_NHPANN"_NCN>AN&<x*<N`N"<NAN>A*N&<x*<NBANNBA$NN`ANAN?AN?AN?AN?~NNA텚NzNVJBfNANBHA텚NNL8N\HA킦NNPL8NANANBHA텚NNL8N`HA킦NNPL8NANpNN$x' HP <N"_NHPp N"_NHPANN"_NCN>pxNHPp"N"_NHPp N"_NHP <N"_NHPp N"_NHPANN"_NCN>A*N&<x*<NBANNBA$NN`ANAN?AN?AN?AN?~NA*N&<x*<NBANNBA$NN`ANAN?AN?AN?AN?~N <r$<ANN\N"<NAN>AN&<x*<N`N"<NAN>N <r$<ANN\N"<NN$aucune solutionN>N`NvANNN|JBfNNN`ANrA8NANANN\HAN&<8<*<NBL8NANpNNm HP <N"_NHPp N"_NHPANN"_NCN> <r$<ANN\Nr NAN>pNܬpNpNprNBgAN??<AN?~NpNpNprNpNܬp NAN&<x*<N6HA킦NvNXHANA"NN\L8NBL8N\A텚NANANN\zN JBfNpNANBHA킦NNPL8NANNx' = xHPp"N"_NHPp N"_NHP <N"_NHPp N"_NHPANN"_NCN>AN&<x*<N`N"<NAN>A*N&<x*<NBANNBA$NN`ANAN?AN?AN?AN?~NNA텚NzNVJBfNZANBHA텚NNL8N\HA킦NNPL8NANANBHA텚NNL8N`HA킦NNPL8NANpNN$x' HP <N"_NHPp N"_NHPANN"_NCN>pxNHPp"N"_NHPp N"_NHP <N"_NHPp N"_NHPANN"_NCN>A*N&<x*<NBANNBA$NN`ANAN?AN?AN?AN?~NA*N&<x*<NBANNBA$NN`ANAN?AN?AN?AN?~N <r$<ANN\N"<NAN>AN&<x*<N`N"<NAN>N <r$<ANN\N"<NN$aucune solutionN>NV$g2N!A8NN\pNܬpNN`ANrpNpNprNBgAN??<AN?~NANANN\HAN&<8<*<NBL8NANNm HP <N"_NHPp N"_NHPANN"_NCN> <r$<ANN\Nr NAN>N`NvANNDJBfN!N`ANrA8NBgAN??<AN?~NANANN\HAN&<8<*<NBL8NANNm HP <N"_NHPp N"_NHPANN"_NCN> <r$<ANN\Nr NAN>NV$gp NpNpNprNN NdLAN ZA N TA$N TpNpNpNܬBmA 0BmA$NA NN\&<x*<NA*NNAHNA$N&<x*<N JBfN#DpC튼NjHpC.NjL8NHAHN&<x*<N6L8NBHpC튼NjHpC.NjL8NAHNNBL8N`HpC튼NjHpC.NjL8NL8N`ANNN#pC튼NjHpC.NjL8NANNA$ 0 <r$<A$NVA$NC튼NjHA$NC.NjL8NHA$NAHNNNVJfpNpNpNܬNHA$NrN`ANrA$NzNVpJBgp/A$N&<x*< N\pJBgp/ANzNVpJBgp/AN&<€x*<N\pJBgp$fN'BgAN??<AN?~NA$N?BgA$N??<~NpN0N'pN0NHA$NrN`ANrNHNvHA$NL8N\zNpJBgp/N`NvHANL8N\zNpJBgp$fN(JN)*A"NA$NzNVpJBgp/A$N&<x*< N\pJBgp/ANzNVpJBgp/AN&<€x*<N\pJBgp$fN)$BgAN??<AN?~NA$N?BgA$N??<~NpN0N)*pN0NV/AN&<€x*<N\pJBgp$grprN <"<N,BgAN??<AN?~NA$N?BgA$N??<~NN\A"NNzpNNVJfpNܸpN <h"<NN$)Choisissez l'unit sur l'axe (Ox) (en cm)N>A.xN CpN~p("<,NAN>Bm:pN~pN <h"<NN$)Choisissez l'unit sur l'axe (Oy) (en cm)4N>A.xN CN NdA3JN A CN>Bm|NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp$fN1TNHNvH <r$<L8N\&<x*<NN&&<x*<N`A NN`NvH <r$<L8N\&<x*<NN&&<x*<N`A$NA6NA NNDpJBgp/ABNA$NNDpJBgp$fN1 ?<2?<A("N" <r$<A NN\&<x*<NB&<x*<N`H <r$<A$NN\&<x*<NB&<x*<N`H <r$<HtH <r$<HA N/A$NC~NHPA5bN C A6 0C$AB 0NzNV$fN1NA N/A$NC~NCN>Ax 0N1A6NzNDJBfN1?<2?<A("N"Bm:BmFNV$gAxN&<x*<N JBgA N&<x*<NDpJBgp/A$N&<x*<NDpJBgp$fN20A N/A$NC~NN.AAN 0N2NUNIT SUR L'AXE (Oy) =CN>AN 0ANN"<,NAN>Bm <r$<HANNH <r$<H <2<$<H <r$<HAuVN CjA< 0N NdpNpNpr2N <r7N,pr2Np"<N, <r2N <"<N,p"<N <"<N,A$ 0 <r$<A$NV <r$<A$NN\&<x*<NB&<x*<N`ANNA 0 <r$<A NV <r$<A NN\&<x*<NB&<x*<N`AHNAHNHANNHA N/A$NC~NHA N/A$NC~NHA N/A$NC ~NHA N/A$NC~NHPA5bN N`NqN`Nq?<2?<?<9?<8A(" NN Nd"_AN LATN ZLANN ZLAHN ZLANN ZLAHN ZpNܸAHNNpNANNNAHN/ANN"NAHN&<x*<N`N/ANN&<x*<N`N"N,pNܸATNN~pNpNp NAHN&<x*<N`HANNvvNXL8N\N/ANN&<x*<N`N"NAN>N NdNDpNܬpN~pNpNpNp("<NN$crire un nombre avec atariN>pN~pNpNp NpFrNN$ Ces trois exemples vous suffiront :N> <r NN6Pour crire ,tapez successivement 1 / 2 ENTERN> <r$<H <r$<Hp1NHPp2NHPtHtHtHAQ <r$<H <r$<HN$-32 HPN$625 HPtHtHtHAQ <r$<H <r$<HN$2R2-1 HPNR3HPtHtHtHAQN NdLAN ZLA킠N ZLA킚N ZLANN ZLAHN ZN\A>N AJN A2N ADN ARN TA:N TA@N TpNpNprNA킲NNܬCHA 0CNA 0ALN NCN>HmA "_NJBgNNCN>pNܸHmpLN"_NJBfNNN>CXAd 0ALN A>CN>A 0CdAX 0AN&<x*<N`ANNA킬NNܬpNpNANANN`N/ <r$<ANN\N"NAXNANN`HARNL8N\N/ <r$<ANN\N"NpNpNpNܬHmpAN"_NpJBgp/HmpN"_NpJBgp$fN=RA킬NNANH <r$<ANN\HA^NAXNN ANN`&<x*<N`HAN&<x*<N`HA~4N ALN Hmp-N"_NpJBgp/Hmp+N"_NpJBgp$fN?ANHmDp-N"_NpJBgp/HmDp+N"_NpJBgp/HmDpRN"_NpJBgp$fN> A CN>N?A CnN>HmA "_NJBfN>A4N&<x*<N JBfN>A:N/A@N"NA:N&<x*<N`HAJNNvvNXL8N`N/A@N"NBm8A CJN>HmA "_NpJBgp/Hmp-N"_NpJBgp$fN?HmA"_NCN>AHN/ANN"NAN>AHN&<x*<N`AHNANzN JBfN?AXN&<x*<N`AXNN?A^N&<x*<N`A^NHmpRN"_NJBfNBANNvANNtpJBgp/ANNBA CnN>HmpRN"_NCN>A4 0AHN&<x*<N`AHNANzN JBfN@AXN&<x*<N`AXNNAA^N&<x*<N`A^NA킲NNܬAHN/ <r$<ANNN\N"NAHN&<x*<N`N/ANN"NAHN&<x*<N`N/ANN"NAHN&<x*<N`N/ <r$<ANNN\N"NAHN&<x*<N`A:N <r$<ANNN\A@NAHN&<x*<N`AHNANzN JBfNBAXN&<x*<N`AXNNBA^N&<x*<N`A^NHmp N"_NpJBgp/Hmp/N"_NpJBgp$fNEAC2N>AN*HPpRN"_NJBfNC8p1NHPA"_NCN>Hmp"_NPHPN-R"_NJBfNCzN-1HPA"_NCN>ANAN.zN pJBgp/HmDp0N"_NpJBgp/HmDp9N"_NpJBgp$fNCA CN>NEANzN JBfNEA 0A킬NNANH <r$<ANN\HAXNANN`&<x*<N`HAN&<x*<N`HA~4N pNܸANH <r$<ANN\HHm2AMN pNpNAN/ <r$<ANN\N"NAXNANN`N/ <r$<ANN\N"NpNpNA2CN>Bm8CAH 0AN&<x*<N`ANNA C2N>A CJN>A CnN>A2CN>Hmp0N"_N pJBgp/Hmp9N"_N pJBgp$fNGANNvANNVpJBgp/AJNNvA킠NNVpJBgp/AnNNvA킚NNVpJBgp$fNFA CN>NGHmA"_NCN>A4N&<x*<N JBfNFHmJA"_NCJN>NGHmnA"_NCnN>AHN/ANN"NAN>AHN&<x*<N`AHNANzN JBfNGAXN&<x*<N`AXNNGA^N&<x*<N`A^NA^NAXNN ANAN&<x*<N JBfNHpNpNAN/ <r$<ANN\N"NANANN`N/ <r$<ANN\N"NpNpNANAXNNVJBfNHAXNANN\ARNHmp N"_NJBgANzN pJBgp/HmA "_NpJBgp/ANANzN JBfNKACN>p1NCN>AN&<x*<N JBfNLACVN>HmVAWN ACVN>HmVAVN AjNzN JBfNLA킬NNANH <r$<ANN\HA^NAXNN ANN`&<x*<N`HAN&<x*<N`HA~4N N::N NdCAH 0CAN 0BmBm8Bm\BmbA CN>A CN>A CN>A CJN>A CnN>N Nd"_AN LANN ZLAHN ZA텎N&<x*<N JBfNMdNQ4A`N TA:N TA@N TAPN AN AN 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ZLAN ZLAN ZLAN ZAN/AN"NAN/AVN"N&AN/AN"NAN/AVN"N N NdLA N ZLA"N ZLANN ZLAHN ZAHN/ANN"NA"NAHNN`N/A"NANNN`N"N,AHN/ANN"NA"NAHNN`N/A"NANNN`N"NA"NvNXAHNN`H <r$<L8N\N/ <r$<&<x*<NA"NNBANNN`N"NA NNN>N NdA` 0ANzNDJBfN,ANANNN&ANNBANN\A`NCA 0C`A 0A`NzN JBgN:A 0N NdA` 0ANAA CN>A CN>A텂N&<x*<N JBfN$AN BmNDpN~pNpNp NHxN6La mmoire doit etre pleine| |ou erreur non prvue ! |HPNretourr"_ NAvNr)| A CN>A CdN>A CN>A C"N>A C N>A C퉴N>A C퉐N>A C(N>N Ndinfo information-------------123456sys_N_P un peu de cours donne d'un systme de n quations p inconnues ATARI rsout votre dmarche rappel du systme recommencer la rsolution du systme 2_degr un peu de cours formules donne d'un polynome du 2_nd degr rsolution algbrique de P(x) = 0 P(x) > 0 P(x) < 0 P(x) >= 0 P(x) <= 0 factorisation rsolution algbrique de P(x) = m minimum ou maximum de P(x) polynome remarques et contraintes sur P(x) donne d'un polynome quelconque rsolution de P(x) = 0 graphe courbe d'quation y = P(x) ancien graphique + courbe y = P(x) impression du graphique rsolution graphique de P(x) = m conserver le graphique rappeler le graphique aide crire un nombre avec ATARI conserver la page texte rappeler la page texte calcul de P(a) avec a = ? effacer STOP quitter le programme ***0.512345678910autre000000000000111111111111444444444444Li->aLiLi->Li<->LjCi<->CjPivot hPivot bArretCours1R^j"x@x\ > \N\"  $ފފފފފ(L  r: hD8~~ &V`:>fd$ (z"D(zR(z^(X(zj(z(z" D h~.DJJ8D(^ @( Rv\J (D:  ,F\ $8$N( $D.dV"N0""2"0* $4"~::L NV2JF>zX΂$ dHnV"<"(8  "(6 B.ZTn(\6 2B."ڴnĴDtrnX"njR hF **60FT\HܾB Nt0FT\H(: v6F.vfrHƄ4 v6F.vfrH. v6,J4. 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FV 7p&N9l/h8,:,L/d4,pĴ@cS@9@p4,rŴAcBSA9Ar`8pJ, 7fnJ/^k0 Eg$2,/h pg  qfH9A/hpjNܰ`A 0 <r$<A NV?<Bg?<O?<MBgB -8/?<NqANr?<Bg?<O?<BgB -8/?<NqANrAN&<x*<N pJBgp/AN&<x*<N pJBgp/AN&<x*<N pJBgp/AN&<x*<N pJBgp$VHg N N2N`NqAN&<x*<N pJBgp/AN&<x*<N pJBgp/AN&<x*<N pJBgp/AN&<x*<N pJBgpF$NqN3HxN$|Cette disquette a |un problemeHPN$finr"_ NANrNd?<NNTSfN4LHxN: Ce programme ne fonctionne| | qu'en moyenne rsolution !|HPN$O K4r"_ NAvNrNd)|| A CN>A텂N&<x*<N JBfN9AN A CN>A}N A텂 0A P0 <r$<A NVA N/p"NXA N/ <r$<C틈NN`NqNqAN AeN prNXHx <r$<C틈NprNXHx <r$<C틈NA 00 <r$<A NVA N/p"NXA N/ <r$<C틈NN`NqNqpr"NXHx" <r$<C틈NA 0 <r$<A NVA N/p"NXA N/ <r$<C틈NN`NqNqpr0NXHx0 <r$<C틈NANAN pNJ gNAfN AfN pr'NXHx' <r$<C틈Npr)NXHx) <r$<C틈NpNJ gN@A 0A$ 0AfN A>N A}N A 00 <r$<A NVA N/p"NXA N/ <r$<C틈NN`NqNqA P0 <r$<A NVA N/p"NXA N/ <r$<C틈NN`NqNqpr"NXHx" <r$<C틈Npr%NXHx% <r$<C틈Npr(NXHx( <r$<C틈Npr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈Npr0NXHx0 <r$<C틈Npr'NXHx' <r$<C틈NA텂N&<x*<N JBfN@BmA CN>AN AN A CN>pNJ gNBjAfN A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpr'NXHx' <r$<C틈Npr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈NAN A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpNJ gNCAfN A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpr'NXHx' <r$<C틈Npr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈NA*N A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpNJ gNENAfN A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpr'NXHx' <r$<C틈Npr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈NA6N A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpNJ gNFAfN A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpr'NXHx' <r$<C틈Npr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈NACvN A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpNJ gNH6AfN BmA 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpr'NXHx' <r$<C틈Npr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈NAPN A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpNJ gNIAfN A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpr'NXHx' <r$<C틈Npr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈NAlN A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpNJ gNKAfN BmA 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpr'NXHx' <r$<C틈Npr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈NA\N A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpNJ gNLAfN A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpr'NXHx' <r$<C틈Npr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈NA\N pNJ gNLhpr!NXHx! <r$<C틈NAZN AN pNJC틾NHPN$! donne d'un polynome quelconque "_NJBfNNNDAZN A}N A|N A P0 <r$<A NVA N/p"NXA N/ <r$<C틈NN`NqNqA 00 <r$<A NVA N/p"NXA N/ <r$<C틈NN`NqNqpr%NXHx% <r$<C틈Npr'NXHx' <r$<C틈Npr(NXHx( <r$<C틈Npr"NXHx" <r$<C틈Npr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈Npr0NXHx0 <r$<C틈NA텂N&<x*<N JBfNNBmA CN>AN AN pNJ "gNOVAZN AN pr'NXHx' <r$<C틈Npr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈NpNJC틾NHPN courbe d'quation y = P(x) "_NJBfNP`AfN AN Hx. <r$<C틈NHx' <r$<C틈NHx) <r$<C틈NHx& <r$<C틈NAN C$A텠 0CA텦 0C*A 0CA 0AN A&NpNJ &gNQpr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈NAfN A&NC텠A$ 0C텦A 0CA* 0CA 0A$N&<x*<N JBfNQA 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqA$NHAN AN A&NpNJ 'gNRHxN$Imprimante branche ?| yHPN$oui|non4r"_ NANrAN&<x*<N JBfNRpNZpNpNpNprNp "<N,pNܸprN <"<N,NrprN <"<N,pNܸpNVA틾NA}N pNJ (gNUAfN pNZA텔 0A$N&<x*<N JBfNSA 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqA 0A$N&<x*<N JBfNT0pC튶NjHpC(NjL8NA킦NpC튶NjHpC(NjL8NANpC튶NjHpC(NjL8NA"NNTpC튶NjHpC(NjL8NA킦NpC튶NjHpC(NjL8NANpC튶NjHpC(NjL8NA"NAN AN AN AN pNVA틾NHx. <r$<C틈NHx) <r$<C틈NHx. <r$<C틈NHx' <r$<C틈NA}N )|8 JNzp NpNpNprNAN pNJ )gNUANpr*NXHx* <r$<C틈NC$A텠 0CA텦 0pNJ *gNV@AfN ANpr'NXHx' <r$<C틈Npr.NXHx. <r$<C틈NpNJ -gNVA2N pr'NXHx' <r$<C틈NpNJ .gNVANpr/NXHx/ <r$<C틈NC톴A 0pNJ /gNWJAN~N fZpNܸANpr'NXHx' <r$<C틈Npr)NXHx) <r$<C틈NpNJ 1gNX8NDpNpNpNprN <"<N,pr'NXHx' <r$<C틈Npr)NXHx) <r$<C틈Npr.NXHx. <r$<C틈NA텂N&<x*<N JBfNX8prNXHx <r$<C틈NpNJC틾NHPN$ calcul de P(a) avec a = ? 4"_NJBfNdA$N&<x*<N JBfNXAN NdXA 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqpNpNpNpNܸprN <"<N,pNprZN <"<&N&pNܸpN~pNpNpNp-rdNN$Soit calculer P(a) avec :4N>pN~pNpNpNpNܬpNpA"<NNP(x) =N> <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN p_"<NNa =N>A킬 0BmpNܬ <r$<H <r$<H <r$<H <r$<H <r$<HA5`N ACN>ACN>pNpP"<Npi"<N, <r$<H <r$<HHmHmtHtHtHALN HmHmAi>N A텎N&<x*<N JBfN\LHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NBmNdACN>ACN>HmAQN CjA톨 0HmAQN CjA텲 0A텲NA톨NN&<x*< NVJBfN]ZHxN$9Prenez un nombre raisonnable.| |Limites : -1000 +1000HPN$O.Kr"_ NANrNDpr.NXHx. <r$<C틈NNdpN~p}rdNN$ RPONSE :eN>pN~ <rdNN$ P(a) =4N>pC(NjHpC(NjL8NBHpC(NjL8NBA텲NNBA텲NNBNCN>HmHmAeN A텎N&<x*<N JBfN^HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NBmNdA퇘CN>HmpC튶NjHpC(NjL8NBHpC(NjL8NBNHPAeN A텎N&<x*<N JBfN_HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NBmNdA퇘CN>HmpC튶NjHpC(NjL8NBHpC(NjL8NBA텲NNBNHPAeN A텎N&<x*<N JBfN`|HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDBmNdHmHmAc N A텎N&<x*<N JBfNa,HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDBmpr.NXHx. <r$<C틈NNdAtCN>HmpC튶NjHpC(NjL8NBHpC(NjL8NBA텲NNBA텲NNBNHPAc N A텎N&<x*<N JBfNb8HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NBmNdAtCN>HmHmAi>N A텎N&<x*<N JBfNbHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDBmpr.NXHx. <r$<C틈NNdACN>ACN>HmAQN pNܬAN )mNc <r$<H <r$<HHmHmtHtHtHALN Nc <"<NN,(l'criture du nombre dpasse le cadre fix)N>AjNN&AjNNDJBfNdXN$( valeur approche : tHPAN.AjNNN"_NHPN )"_NCN> <"<NAN>pr'NXHx' <r$<C틈Npr.NXHx. <r$<C틈Npr)NXHx) <r$<C틈NpNJC틾NHPN quitter le programme "_NJBfNe|HxN$-Souhaitez vraiment quitter| |ce programme ? |4HPN$non|oui4r"_ NAvNrAvN&<x*<NDJBfNe|NdN NdNDpN~pNpNp NA*N N NdNDpNܸNzpNpNpNprN <"<N,pNpNp NpNpNprNp r}NpF"<N&pN~pNpdNp2NNSYSTEMES LINEAIRESCN>pNܸp2"<NAN>A 0 <r$<A NVpNܸA N&<x*<N`N/A N&<x*<N`N"NAN>N`NqNqBgBg?<?<A2" NpNܸNzpN~pNpNpNNn quations ( 1 < n < 7 )CN>Np inconnues ( 1 < p < 7 )CN>pNpNpNpNܬ <r$<H <r$<H <r$<H <r$<HAyN pd"<NAN>pNpNpNpNܸpN~pNpNpNpNpN?<K?<?<?<A" NA 0 <r$<A NV <r$<A NN\&<x*<NB&<x*<N`H <r$<H <r$<HA NHAzN N`~Nq <r$<H <r$<H <r$<HAN pNܸCxAZ 0pN~pNpNpNpd"<NN$n quations n = N>pd"<NAZNNN>CZAl 0?<P?<uA"N"pNpN <r$<H <r$<H <r$<H <r$<HAyN pN~pNpNpN <"<NAN>pNܸpNpNpN~pNpNpNA 0 <r$<A NV <r$<A NN\&<x*<NB&<x*<N`H <r$<H <r$<HA NHAzN N`~Nq <r$<H <r$<H <r$<HAN pNܸCxA 0NDA퀖N TA퀐N TA퀜N TA퀢N TA퀨N TA퀮N TA퀺N TpNpNpNprN <"<vN,pN~pNAZN&<x*<NB&<x*<N\vNXN&&<x*<N`A퀄NAN&<x*<NB&<x*<N\vNXN&&<x*<N`A퀊NAN&<x*<NBA퀊NN`H <r$<L8N\A퀮NA퀮N&<x*<N`A퀺NA 0AZNANVAT 0ANATNVpaNHPp N"_NHPAN&<x*<N`NN"_NHPATN&<x*<N`NN"_NCN>pxNHPp N"_NHPATN&<x*<N`NN"_NCN> <r$<ATNN\&<x*<NBA퀊NN`A퀖N <r$<ANN\&<x*<NBA퀄NN`A퀐NA퀖N&<x*<N`A퀜NC퀐A퀢 0N4A퀖N/A퀐N"NAN~N4A퀜N/A퀢N"NAN~A퀜N&<x*<N`A퀨NATN&<x*<NtpJBgp/ANATNNVpJBgp$fNo~N4A퀨N/A퀐N"Np+NN`NqN4A퀮N/A퀐N"Np=NN4A퀺N/A퀐N"NpbNHPp N"_NHPAN&<x*<N`NN"_NN~AN&<x*<NBN&vNXA퀊NN`A NC퀐AJ 0N`NqpN~pNpNpN <rdNN6Cofficients et constantes sont des nombres RATIONNELSN>pNܬ?<?<?<?<~NAq N pNpNpN <rN <"<N,AN N NdAZN/ANC>~N.AZN/ANCn~N.AZN/ANCD~N.AZN/ANCt~N.AZNCJN,AZNCPN,AZNCzN,AZNC튀N,AZNC튆N,AN&<x*<N`NC튤N,AZN/ANC튘~N.ANC튪N,ANChN,ANC튰N,A 0ANA NVA N/A NChNN`NqNqAJN&<x*<N`AJNA 0pNܬA 0AZNANVAT 0AN&<x*<N`ATNVAN N`NqNqN`NqNqBmN NdAN TAN TNDpNpNN4p r NNN0QUELQUES INSTANTS !NCZA 0A 0AN A큰 0ANAZNN `A큰NVBmANHAN AN&<x*<N JBfNtA큰NA큞NNDJBfNt\C큰Az 0C큞A 0AN A큰N/A큰NCD~NANA큰N/A큰NC>~NANA큰NHAʂN AN NuA큰N&<x*<N`A큒NANA큰NNVJBfNuA큒NHATN AN&<x*<N JBfNurA큒NHA큰NHAN NsNuA큒N&<x*<N`A큒NAN&<x*<N`A큒NNVJBfNuNu N`NqANAZNN `A큰N <r$<&<x*<A큰NA큰N/A큰NC>~NzNDJBfNvJAN N`NqNqBmAT 0ANATNVAZN/ATNC>~NzN JBfNvAN&<x*<N`ANN`NqNqANANN JBfNw>AZNCJNjzN JBfNw: <r$<AZNN\AZNNvTNw>BmANAZNNVpJBgp/ANzNDpJBgp$fNwA 0AN&<x*<N`ANNDpNpNN$CVotre systme quivaut au systme dont la matrice est la suivante :CN>AN pN~pNpNpNAT 0ANATNVATNC튰NjH <r$<L8N\N/ <r$<A퀐NN\N"NpxNN>ATNC튰NjH <r$<L8N\N/ <r$<A퀐NN\N"NATNChNjNN>N`0NqpN~pNpNpNAN~N y^z|zN NdNIl n'a donc pas de solution.CN> <r$<A퀐NN\Nr NAN>A퀐N&<x*<N`H <r$<AZNN\&<x*<NBL8N`Nr NAN>pNܬpNpNprNAtN/ <r$<AZNN\&<x*<NBA퀐NN`&<x*<N`N"NA큌N/ <r$<AZNN\&<x*<NBA퀐NN`&<x*<N`N"NN NdN"Il admet donc une unique solution.CN> <r$<A퀐NN\Nr NAN>A퀐N&<x*<N`H <r$<AZNN\&<x*<NBL8N`Nr NAN>pN <r$<H <r$<H <r$<H <r$<HAunN AN pN~pNpNpN <r$<A퀐NN\NrdNN$ Que voici ...&N>pNN NdN(Il admet donc une infinit de solutions.CN> <r$<A퀐NN\Nr NAN>A퀐N&<x*<N`H <r$<AZNN\&<x*<NBL8N`Nr NAN>pN <r$<H <r$<H <r$<H <r$<HAunN AN AZN&<x*<N`ATNANATNVA 0AZNANVAN/ATNC>~NzNVJBfN~ATNC튰NjHAN/ATNC튘~NvNXL8N\H <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"Np-NN>NAN/ATNC>~NzN\JBfNATNC튰NjHAN/ATNC튘~NvNXL8N\H <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"NN N>AZN&<x*<N`ATNN\JBfNATNC튰NjHAN/ATNC튘~NvNXL8N\H <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"Np+NN>AN/ATNC>~NHAN/ATNCD~NL8NB&<x*<N pJBgp/AN/ATNC>~NzN pJBgp$fNATNC튰NjH <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"NN N>AN/ATNC>~NzNDJBfNATNC튰Nj&<x*<N`N/ <r$<ANN\&<x*<NBA퀐NN`N"NpxNN>ATNC튰Nj&<x*<N`N/ <r$<ANN\&<x*<NBA퀐NN`&<x*<N`N"NATNChNjNN>N` NqN`NqA 0AZNANVANCJNjzNtJBfN2p+NCN>N@p-NCN>ANC튰Nj&<x*<N`HAN&<x*<N`NC튤NjvNXL8N`AHNANC튪NjvNXAHNN\H <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"NN N>ANC튪NjvNXAHNN\H <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"NAN>N`:NqpN~pNpNpNA퀐N&<x*<N`H <r$<AZNN\&<x*<NBL8N`Nr N <"<N, <r$<A퀐NN\NrdNN$ Que voici ...&N>pNN Nd <r$<A퀐NN\NrN <r$<A퀐NN\N"<N, <r$<A퀐NN\Nr NNL N>A퀐N&<x*<N`H <r$<ANN\&<x*<NBL8N`Nr NA퀐N&<x*<N`H <r$<ANN\&<x*<NBL8N`N"<N,AT 0AZNATNVA 0 <r$<ATNN\ANVATNC튰NjH <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"Np NN>N`~NqATN&<x*<N`ANAZNANVATNC튰NjH <r$<L8N\N/ <r$<ANN\&<x*<NBA퀐NN`N"Np NN>N`~NqATNC튰NjH 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<r$<ATNN\&<x*<NBA퀊NN`vNX&<x*<N`N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N, <r$<ATNN\&<x*<NBA퀊NN`vNXH <r$<L8N\A퀖NAN&<x*<NBA퀄NN`vNXH <r$<L8N\A퀐NpNܬpN~pNpNpNpNܸpNpNpN <r$<A퀖NN\N/ <r$<A퀐NN\N"N <r$<A퀖NN\N/A퀐N&<x*<N`N"N,ANzN\JBfNǜp-NCN>ANBANNǪp+NCN>pNܬATN&<x*<NVpJBgp/Hmp-N"_NpJBgp$fN. <r$<A퀖NN\N/A퀐N"NAN>C퀖AH 0C퀐AN 0ANANNB&<x*<NDpJBgp/ANzNDpJBgp$fNAHNHANNHANHANHAN Nz <r$<ATNN\&<x*<NBA퀊NN`vNXA퀖NAN&<x*<NBA퀄NN`vNXH <r$<L8N\A퀐NpN~pNpNpNpNܸpNpNpN <r$<A퀖NN\N/ <r$<A퀐NN\N"NA퀖N&<x*<N`N/A퀐N&<x*<N`N"N,C퀖AH 0C퀐AN 0AHNHANNHANHANHA"N N NdLA N ZA 0ANANVA N/AN/A N/ANC>~NANNBC>~N8A N/AN/A N/ANCD~NANNBCD~N8A N/ANC>~NA~NA~N8A N/AN/A N/ANCD~NA~NHA$N/ANCD~NL8NBC>~N8A N/AN/A N/ANC>~NHA$N/ANC>~NHA N/ANCD~NL8NBL8N`C>~N8A N/AN/A N/ANCD~NHA$N/ANCD~NL8NBCD~N8A N/ANC>~NA~NA~N8A N/AN/A N/ANCD~NA~N8AN/AN/ANC\NjCD~N8N`NqNqAN/AN&<x*<N`NCVNjCJNAN/AN&<x*<N`NC\NjCPNAVNA\NN NdA 0ANANVAN/ANC>~N/AzN/ANC>~N"_NXAN/ANCD~N/AzN/ANCD~N"_NXN`zNqANCJN/AzNCJN"_NXANCPN/AzNCPN"_NXN NdLA$N ZLA N ZAT 0AZNATNVATN/A NC>~N/ATN/A$NC>~N"_NXATN/A NCD~N/ATN/A$NCD~N"_NXN`zNqA NChN/A$NChN"_NXN NdLA$N ZAN&<x*<N`NCVN,AN&<x*<N`NC\N,A 0ANANVAN/A$N/ANC>~NCVNAN/A$N/ANCD~NC\NN`NqNqAN&<x*<N`N/A$NCJNjCVNAN&<x*<N`N/A$NCPNjC\NN NdLA"N ZLANN ZLAHN ZBm|AxNzN JBfNRNHNvHAHNL8N\A"NN\pJBgp/N`NvHANNL8N\HA"NvNXL8NVpJBgp/NVNv&<x*<N pJBgp$fNAx 0NHNvHAHNL8N\H <r$<L8N\A"NN\pJBgp/N`NvHANNL8N\HA"NvNXL8NVpJBgp/NVNv&<x*<N pJBgp$fNAx @0NHNvHAHNL8N\H <r$<L8N\A"NN\pJBgp/N`NvHANNL8N\HA"NvNXL8NVpJBgp/NVNv&<x*<N pJBgp$fNتAx 0NHNvHAHNL8N\H <r$<L8N\A"NN\pJBgp/N`NvHANNL8N\HA"NvNXL8NVpJBgp/NVNv&<x*<N pJBgp$fN|Ax 0NHNvHAHNL8N\H <r$<L8N\A"NN\pJBgp/N`NvHANNL8N\HA"NvNXL8NVpJBgp/NVNv&<x*<N pJBgp$fNNAx @0`N NdpNܬpNp NprN <"<N <"<N <"<N <"<N <"<^N <"<N <"<^N <"<NpNpNprN <"<N <"<N <"<N <"<N <"<^N <"<^N <"<N <"<NpN~pNpNpNN$ouilCN> <"<NAN>N$nonCN> <"<kNAN>N NdBm|AxNzN JBfNݰNHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx 0NݬNHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNݨAx 0NݬBm|`RN NdAHN TANN TA>N TA> 0AH H0AN 0Bm|AxNzN JBfNPNHNvHAHNL8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx 0NHNvHAHNL8N\H <r$<L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNߐAx 0NHNvHAHNL8N\H <r$<L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNZAx @0NHNvHAHNL8N\H <r$<L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fN$Ax 0NHNvHAHNL8N\H <r$<L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx 0NHNvHAHNL8N\H <r$<L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx @0NHNvHAHNL8N\H <r$<L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx `0NHNvHAHNL8N\H <r$< L8N\A>NN\pJBgp/N`NvHANNL8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNLAx 0`A4N N NdpNܬpNp NprN <"<^N <"<N <"<^N <"<N <"<N <"<N <"<N <"<NpNpNprN <"<^N <"<^N <"<N <"<N <"<N <"<N <"<N <"<NpN~pNpNpNN$ouilCN> <"<kNAN>N$nonCN> <"<NAN>Bm|AxNzN JBfNNHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx 0NNHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp/NVNv&<x*<N pJBgp$fNAx 0NBm|`RN NdA8N TA>N TADN TBmNA>N&<x*<NtpJBgp/ <r$<ANN\A>NNtpJBgp$fNlN`NvHA퀐NL8N\H <r$<L8N\&<x*<NN&ADNADN&<x*<NtpJBgp/ <r$<AZNN\ADNNtpJBgp$fNlNVSgNlA8 0A>N&<x*<N`ATNADN&<x*<N`AN`"ANATNNtJBfNpNpNpN <r$<ATNN\&<x*<NBA퀊NN`vNXH <r$<L8N\N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N <r$<ATNN\&<x*<NBA퀊NN`vNX&<x*<N`N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N,pNpNpNpN <r$<ATNN\&<x*<NBA퀊NN`vNXH <r$<L8N\N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N <r$<ATNN\&<x*<NBA퀊NN`vNX&<x*<N`N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N,N|pNpNpN <r$<ATNN\&<x*<NBA퀊NN`vNXH <r$<L8N\N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N <r$<ATNN\&<x*<NBA퀊NN`vNX&<x*<N`N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N,pNpNpNpN <r$<ATNN\&<x*<NBA퀊NN`vNXH <r$<L8N\N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N <r$<ATNN\&<x*<NBA퀊NN`vNX&<x*<N`N/AN&<x*<NBA퀄NN`vNXH <r$<L8N\N"N,pN0pNpNpN <"<N <"<N,AN N NdC AH 0CJAN 0pN~pNpNpNpNܸAN&<x*<N`ATNNVJBfNAN&<x*<N`NNHPATN&<x*<N`NN"_NCN>N$a =CN>NAN&<x*<N`NNCN>Nb =CN>AHNvNXH <r$<L8N\ANANNvNXANAN/AN"NAN>pNܸAN&<x*<N`N/AN&<x*<N`N"NAN>AHN&<x*<N`AHNA 0A 0pNܸpN~pNpNpNAN ANATNNtJBfNAN/ATN/ANC>~N8AN/ATN/ANCD~N8AN/ATN/ANCn~N8AN/ATN/ANCt~N8NAN/ANCJNAN/ANCPNAN/ANCzNAN/ANC튀NAN N NdNDpN~pNp Np "<NN$un peu de cours4N>pNpNpr NN$ECes systmes linaires sont rsolus par la mthode du PIVOT DE GAUSS.N>p(r NN$)Li dsignera la Ligne i ,Ci la colonne i. N>pFr NN$Ainsi le systme aN>pZr2NN$2 x + 3 y - 9 z = 84N>pnr2NN$- x + 5 y = 14N> <r2NN$ 3 y - 5 z = 94N>pn"<NN$s'crit4N>pZ"<NN$2 3 -9 84N>pn"<NN-1 5 0 1N> <"<NN$0 3 -5 94N>pNܬpN?<?<P?<|?<U?<|?<?<?<~N?<?<P?<?<~N?<?<P?<&?<U?<&?<?<?<~NpNpZ"<:NNL1N>pn"<:NNL2N> <"<:NNL3N> <"<NN C1 C2 C3N>pNpNpN <r$<H <r$<H <r$<H <r$<HAunN NDpNp Np "<NN$%oprations sur les lignes et colonnesN>pNpNpNpNpNpr NN$OLi --> a Li : multiplier les cofficients et constante de Li par a(non nul)N>p(r NN>Li --> Li + lj : ajouter les lignes Li,Lj (nouvelle ligne Li)N>p2r NN$-Li<-->Lj : change des lignes Li et LjeN>pCj : change des colonnes Ci et Cj4N>p NpPr NN$UN PETIT PLUS !eN>pNp_r NNHL'option 'PIVOT H' remplace la suite d'oprations Li --> a Li + b Lj quiN>pir NN.permet de mettre des 0 sous un nombre non nul.N>pxr NNHL'option 'PIVOT B' remplace la suite d'oprations Li --> a Li + b Lj quiN> <r NN$5permet de mettre des 0 au-dessus d'un nombre non nul. N>pN <r2NN&Ces oprations transforment un systmeN> <r2NN$en un systme quivalent.eN>pNN Ndpp@pWBg?<NN\pp@pW?<?<NN\pp@pW?<?<NN\pp@pW?<?<NN\A톴 0N NdA>NAnNADNAtNAJNAPNAzNA튀NA튆NA튤NA튘NA튪NAhNA튰NN NdAzN <r$<H <r$<H <r$<H <r$<HAunN AfN N NdpNpNpNprN <"<N,pNܸpN~pNpNpNpr NNLLe polynome P(x) = a x + b x + c (a non nul) peut se mettre sous la formeN>p "<Np2NN>pN~p#r NNP(x) = a [ ( x + ) - ]N>p"<NpbNN>p+"<NN2aN>pNܬ?<?<!?<?<!~Np"<Np2NN>p"<NpNN>p+"<NN4aN>p+"<N <NN>?<?<!?<?<!~NN( HPpN"_NHPN = b"_NHP <N"_NHPN - 4ac : discriminant de P(x) )"_NCN>p#"<,NAN>pN~p NpNpN$Si HPpN"_NHPN* < 0 , P(x) ne s'annule pour aucune valeur"_NCN>N$Si HPpN"_NHPN* = 0 , P(x) s'annule pour une seule valeur"_NCN>N$Si HPpN"_NHPN$1 > 0 , P(x) s'annule pour exactement deux valeurs4"_NC,N>pN~pNpNp_r2NAN>psrFNAN> <rZNA,N>N NdpNܸpNpNpNprN <"<N,pNpNpNp"<Np0"<N&pNp"<Np2"<N&N$P(x) = a x + b x + cCN>pNܸpN~pNpNpNp'"<NAN>pN~pNpNpN <"<NN$A , B ET C SONT RATIONNELS.cN>pN~p "<JNp2NN>pFrdNNAVECN>pP"<NN$a =4N>A2NA킲 0A킬 0 <r$<H <r$<H <r$<H <r$<H <r$<H <r$<H <r$<HA`N HxANC튶NHxANC(NpC튶NjzN JBfNpNpN~p<"<N <"<N&pP"<NNATTENTION ! LE COEFFICIENT aN>pd"<NN$DOIT ETRE NON NULN> <r$<H <r$<H <r$<H <r$<HAunN A2NNpN~pNpNpNpn"<NN$b =4N>A킲 0A킬 0 <r$<H <r$<H <r$<H <r$<H <r$<H <r$<H <r$<HA`N HxANC튶NHxANC(NpN~pNpNpN <"<NN$c =4N>A킲 0A킬 0 <r$<H <r$<H <r$<H <r$<H <r$<H <r$<H <r$<HA`N HxANC튶NHxANC(NA 0 <r$<A NVA N/A NC튶NjC@NA N/A NC(NjCFNN`NqNqN Nd"_ALN "_AFN "_A@N "_A:N "_A4N "_A.N LANN ZLAHN ZHm.Hm4Ai>N AC.N>AC4N>Hm:Hm@Ai>N AC:N>AC@N>HmFHmLAi>N ACFN>ACLN>Hm.p0N"_NJBfN Hm4p1N"_NJBfNHm.p1N"_NJBfNzHm.N-1"_NJBfNTN-xCRN>NpxNCRN>AHNHANNHHm.AHN A.NNvvNXAHNN`&<x*<N`AHNHm.AQN ApN&<x*<NVpJBgp/AjNN&AjNNDpJBgp$fNt <r$<AHNN\HA.NNvvNXL8N\N/ANN"Np(NN>NpxNCRN>NFpxNCRN>Hm.AoN CAX 0Hm4AoN CA^ 0AHNHANNHHm.Hm4tHtHtHALN A^NAXNN AHNN`&<x*<N`AHNApN&<x*<NDpJBgp/Hm4p1N"_NpJBgp/AjNN&AjNNDpJBgp$fN <r$<AHNN\N/ANN"Np)NN>AHN&<x*<N`AHNAHN/ANN"NARN>AHN&<x*<N`A텸NHm.N-1"_NpJBgp/Hm4p1N"_NpJBgp$fN <Ѝ/ <r$< _N pxNCRN>Hm.p0N"_NJBfN ZAHN&<x*<N`AHNA:N*HPp-N"_NJBfN Hm:AdTN AC:N> <r$<AHNN\N/ANN"Np-NN>N 8Hm:p0N"_NJBfN 8 <r$<AHNN\N/ANN"Np+NN>AHN&<x*<N`AHNHm:p0N"_NJBfNHm@p1N"_NJBfN Hm:p1N"_NJBfN Hm:N-1"_NJBfN N-xCRN>N FpxNCRN>AHNHANNHHm:AHN A:NNvvNXAHNN`&<x*<N`AHNHm:AQN ApN&<x*<NDpJBgp/AjNN&AjNNDpJBgp$fN <r$<AHNN\HA:NNvvNXL8N\N/ANN"Np(NN>N pxNCRN>Hm:AoN CAX 0Hm@AoN CA^ 0AHNHANNHHm:Hm@tHtHtHALN A^NAXNN AHNN`&<x*<N`AHNApN&<x*<NDpJBgp/Hm@p1N"_NpJBgp/AjNN&AjNNDpJBgp$fNhAHN/ANN"Np)NN>AHN&<x*<N`AHNAHN/ANN"NARN>AHN&<x*<N`AHNAFN.zNDJBfNAFN.zNVJBfNAHN/ANN"Np+NN>NAFN.BNCFN>AHN&<x*<N`AHNAHNHANNHHmFHmLtHtHtHALN CHA 0AFNNvHALNNvL8N vNXAHNN`&<x*<N`ANN NdA탨N TA탨 0 <r$<A탨NVAFN N`NqNqN NdpNܸpprxN <"<,N&A탨N&<x*<N`NNCXN>HmXN ="_NCXN>pN~ <rxNAXN>pN~BmA킲 @0pNܸ <r$<H <r$<H <r$<H <r$<H <r$<HA5`N HmHmAi>N A탨N/ACNA탨N/ACNHmAQN A탨N/AjNC튶NA탨N/AN.C(NN NdpNpNpNprN <"<N,pNpNpNprZN <"<&N&pNܸpN~pNpNpNp(rdNN$ L'quation 4N>pN~pNpNpNpNܬpNNx HP <N"_NHPN R ,"_NCN>pA"<NAN> <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN ANrANN$= 0N>pC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶NjANpC튶NjANA{N pC튶NjANA{N A 0 <r$<A NVA NC튶N/AN _NN`NqNqpC튶Nj&<x*<N6HpC튶NjvNXHpC튶NjL8NBL8N\A텾NA텾N&< x*<NVJBfNHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NNTpN~pNpNpNpNܬA텾NzN\JBfNpZrdNNn'admet aucune solution.N>A텾NzN JBfNpZrdNN$admet une solution unique , savoirN>pN~pNpNpNpC튶NjBANpC튶NjNPANANNHANNBANANANANzNDJBfNpn"<NAN> <r$<H <r$<HANHANHA"N A텾NzNVJBfNTpZrdNN$admet exactement deux solutions4N>Av 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfNCTAv 0AT 0N`zNqpN~pNpNpNAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fNHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NNTpC튶NjBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N px"<NNx' =N> <r$<H <r$<HHmHmtHtHtHALN pC튶NjBNHPp+N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N <"<NNetN>pxNHPp"N"_NHPN ="_NCN> <"<NAN>HmHmAi>N <r$<H <r$<HHmHmtHtHtHALN N NdpNpNpNprN <"<N,pNpNpNprZN <"<&N&pNܸpN~pNpNpNpFrdNNSoit rsoudre l'quation :N>pN~pNpNpNpNܬpNNx HP <N"_NHPN R ,"_NCN>p_"<NAN> <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN ANr_NN$= mN>pxrdNNavec m =N>BmpNܸ <r$<H <r$<H <r$<H <r$<HtH <r$<H <r$<HA`N CA 0CA 0pNprN <"<N,pN~pNpNpNpNpNpNprZN <"<&N&p(rdNN$ L'quation 4N>pN~pNpNpNpNܬpNNx HP <N"_NHPN R ,"_NCN>pA"<NAN> <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN ANrANp=NN>AN&<x*<N`H <r$<HANNHPANNHPtHtHtHALN HxpC튶NjANNBHpC(NjANNBL8N\C튶NHxpC(NjANNBC(NpC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶NjANpC튶NjANA{N pC튶NjANA{N A 0 <r$<A NVA NC튶N/AN _NN`NqNqpC튶Nj&<x*<N6HpC튶NjvNXHpC튶NjL8NBL8N\A텾NA텾N&< x*<NVJBfN#RHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NN* pN~pNpNpNpNܬA텾NzN\JBfN#pZrdNNn'admet aucune solution.N>A텾NzN JBfN%~pZrdNN$admet une solution unique , savoirN>pN~pNpNpNpC튶NjBANpC튶NjNPANANNHANNBANANANANzNDJBfN$ANANANANA{N <Ѝ/AN _N <Ѝ/AN _NNx' = xHPp"N"_NHPN ="_NCN>pn"<NAN> <r$<H <r$<HANHANHA"N A텾NzNVJBfN* pZrdNN$admet exactement deux solutions4N>Av 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfN&CTAv 0AT 0N`zNqpN~pNpNpNAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fN'HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NN* pC튶NjBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N px"<NNx' =N> <r$<H <r$<HHmHmtHtHtHALN pC튶NjBNHPp+N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N <"<NNetN>pxNHPp"N"_NHPN ="_NCN> <"<NAN>HmHmAi>N <r$<H <r$<HHmHmtHtHtHALN A 0 <r$<A NVA N/A NC@NjC튶NA N/A NCFNjC(NN`NqNqN NdpNpNpNprN <"<N,pNpNpNprpN~pNpNpNpNܬpNNx HP <N"_NHPN R ,"_NCN>p7"<NAN> <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN ANr7NN$> 0N>pC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶NjANpC튶NjANA{N pC튶NjANA{N A 0 <r$<A NVA NC튶N/AN _NN`NqNqpC튶Nj&<x*<N6HpC튶NjvNXHpC튶NjL8NBL8N\A텾NA텾N&< x*<NVJBfN.VHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NN6pN~pNpNpNpNܬA텾NzN\JBfN/pC튶NjzN\JBfN.N$n'admet aucune solution4CN>N/N"admet R pour ensemble de solutionsCN>pPrdNAN>N6A텾NzN JBfN1pC튶NjzN\JBfN/zpPrdNN$n'admet aucune solutionON>N1pPrZNN.admet R priv de x0 pour ensemble de solutionsN>pN~pNpNpNpC튶NjBANpC튶NjNPANANNHANNBANANANANzNDJBfN0ANANANANA{N <Ѝ/AN _N <Ѝ/AN _NpirdNN$ avec x0 =4N> <r$<H <r$<HANHANHA"N N6pC튶NjzNVJBfN1Nadmet l'ensemble ] -HP <N"_NHPN$ ,x'[ u ] xt"_NHPp"N"_NHPN$ , + 4"_NHP <N"_NHPN ["_NCN>Npour ensemble de solutionsCN>N2^N$admet l'intervalle ] x' , xHPp"N"_NHPN [ pour ensemble"_NCN>N de solutionsCN>pPrdNAN>p_rdNAN>pNpsrdNNavecN> <"<NNx' =N> <r}NNetN>pxNHPp"N"_NHPN ="_NCN> <"<NAN>Av 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfN3CTAv 0AT 0N`zNqpN~pNpNpNAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fN4HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDN6pC튶NjBHpC튶NjNHL8NBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N <r$<H <r$<HHmHmtHtHtHALN pC튶NjBHpC튶NjNHL8NBNHPp+N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N <r$<H <r$<HHmHmtHtHtHALN N NdpNpNpNprN <"<N,pNpNpNprpN~pNpNpNpNܬpNNx HP <N"_NHPN R ,"_NCN>p7"<NAN> <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN ANr7NN$< 0N>pC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶NjANpC튶NjANA{N pC튶NjANA{N A 0 <r$<A NVA NC튶N/AN _NN`NqNqpC튶Nj&<x*<N6HpC튶NjvNXHpC튶NjL8NBL8N\A텾NA텾N&< x*<NVJBfN:HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NNCnpN~pNpNpNpNܬA텾NzN\JBfN;pC튶NjzNVJBfN;:N$n'admet aucune solution4CN>N;jN"admet R pour ensemble de solutionsCN>pPrdNAN>NCnA텾NzN JBfN=|pC튶NjzNVJBfN;pPrdNN$n'admet aucune solutionON>N=vpPrZNN.admet R priv de x0 pour ensemble de solutionsN>pN~pNpNpNpC튶NjBANpC튶NjNPANANNHANNBANANANANzNDJBfN=ANANANANA{N <Ѝ/AN _N <Ѝ/AN _NpirdNN$ avec x0 =4N> <r$<H <r$<HANHANHA"N NCnpC튶NjzN\JBfN>VNadmet l'ensemble ] -HP <N"_NHPN$ ,x'[ u ] xt"_NHPp"N"_NHPN$ , + 4"_NHP <N"_NHPN ["_NCN>Npour ensemble de solutionsCN>N>N$admet l'intervalle ] x' , xHPp"N"_NHPN [ pour ensemble"_NCN>N de solutionsCN>pPrdNAN>p_rdNAN>pNpsrdNNavecN> <"<NNx' =N> <r}NNetN>pxNHPp"N"_NHPN ="_NCN> <"<NAN>Av 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfN@JCTAv 0AT 0N`zNqpN~pNpNpNAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fNARHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NNCnpC튶NjBHpC튶NjNHL8NBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N <r$<H <r$<HHmHmtHtHtHALN pC튶NjBHpC튶NjNHL8NBNHPp+N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N <r$<H <r$<HHmHmtHtHtHALN N NdpNpNpNprN <"<N,pNpNpNprpN~pNpNpNpNܬpNNx HP <N"_NHPN R ,"_NCN>p7"<NAN> <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN <NHPN 0"_NCN>ANr7NAN>pC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶NjANpC튶NjANA{N pC튶NjANA{N A 0 <r$<A NVA NC튶N/AN _NN`NqNqpC튶Nj&<x*<N6HpC튶NjvNXHpC튶NjL8NBL8N\A텾NA텾N&< x*<NVJBfNGdHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NNPpN~pNpNpNpNܬA텾NzN\JBfNH&pC튶NjzN\JBfNGN$n'admet aucune solution4CN>NHN"admet R pour ensemble de solutionsCN>pPrdNAN>NPA텾NzN JBfNJpC튶NjzN\JBfNIpPrdNN$admet une unique solution ,x0N>pN~pNpNpNpC튶NjBANpC튶NjNPANANNHANNBANANANANzNDJBfNIzANANANANA{N <Ѝ/AN _N <Ѝ/AN _NpirdNN$ avec x0 =4N> <r$<H <r$<HANHANHA"N NJpPrdNN"admet R pour ensemble de solutionsN>NPpC튶NjzNVJBfNJNadmet l'ensemble ] -HP <N"_NHPN$ ,x'] u [ x4"_NHPp"N"_NHPN$ , + 4"_NHP <N"_NHPN ["_NCN>Npour ensemble de solutionsCN>NKfN$admet l'intervalle [ x' , xHPp"N"_NHPN ] pour ensemble"_NCN>N de solutionsCN>pPrdNAN>p_rdNAN>pNpsrdNNavecN> <"<NNx' =N> <r}NNetN>pxNHPp"N"_NHPN ="_NCN> <"<NAN>Av 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfNLCTAv 0AT 0N`zNqpN~pNpNpNAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fNMHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NNPpC튶NjBHpC튶NjNHL8NBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N <r$<H <r$<HHmHmtHtHtHALN pC튶NjBHpC튶NjNHL8NBNHPp+N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N <r$<H <r$<HHmHmtHtHtHALN N NdpNpNpNprN <"<N,pNpNpNprpN~pNpNpNpNܬpNNx HP <N"_NHPN R ,"_NCN>p7"<NAN> <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN <NHPN 0"_NCN>ANr7NAN>pC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶NjANpC튶NjANA{N pC튶NjANA{N A 0 <r$<A NVA NC튶N/AN _NN`NqNqpC튶Nj&<x*<N6HpC튶NjvNXHpC튶NjL8NBL8N\A텾NA텾N&< x*<NVJBfNTHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NN\pN~pNpNpNpNܬA텾NzN\JBfNTpC튶NjzNVJBfNTN$n'admet aucune solution4CN>NTN"admet R pour ensemble de solutionsCN>pPrdNAN>N\A텾NzN JBfNVpC튶NjzNVJBfNVpPrdNN$admet une unique solution ,x0N>pN~pNpNpNpC튶NjBANpC튶NjNPANANNHANNBANANANANzNDJBfNVANANANANA{N <Ѝ/AN _N <Ѝ/AN _NpirdNN$ avec x0 =4N> <r$<H <r$<HANHANHA"N NVpPrdNN"admet R pour ensemble de solutionsN>N\pC튶NjzN\JBfNWNadmet l'ensemble ] -HP <N"_NHPN$ ,x'] u [ x4"_NHPp"N"_NHPN$ , + 4"_NHP <N"_NHPN ["_NCN>Npour ensemble de solutionsCN>NXN$admet l'intervalle [ x' , xHPp"N"_NHPN ] pour ensemble"_NCN>N de solutionsCN>pPrdNAN>p_rdNAN>pNpsrdNNavecN> <"<NNx' =N> <r}NNetN>pxNHPp"N"_NHPN ="_NCN> <"<NAN>Av 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfNYCTAv 0AT 0N`zNqpN~pNpNpNAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fNZHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NN\pC튶NjBHpC튶NjNHL8NBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N <r$<H <r$<HHmHmtHtHtHALN pC튶NjBHpC튶NjNHL8NBNHPp+N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N <r$<H <r$<HHmHmtHtHtHALN N NdBmpNܸpNpNpNprN <"<N,pNpNpNprZN <"<&N&pNܸpN~pNpNpNpC튶NjzNVJBfN]N Le minimum du polynome suivant :CN>N]N Le maximum du polynome suivant :CN>p-rdNAN>pN~pNpNpNpNܬpNpF"<NNP(x) =N> <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN p_rdNN est atteint pour la valeurN>pC튶NjBHpC(NjL8NBNHPpC(NjNPHpC튶NjL8NBNHPAi>N <r$<H <r$<HHmHmtHtHtHALN pxrdNN et vaut N>AN.A텲NACN>pC(NjHpC(NjL8NBHpC(NjL8NBA텲NNBA텲NNBNCN>HmHmAeN A텎N&<x*<N JBfN`HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NBmNfA퇘CN>HmpC튶NjHpC(NjL8NBHpC(NjL8NBNHPAeN A텎N&<x*<N JBfNaHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NBmNfA퇘CN>HmpC튶NjHpC(NjL8NBHpC(NjL8NBA텲NNBNHPAeN A텎N&<x*<N JBfNbHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NBmNfHmHmAc N A텎N&<x*<N JBfNcJHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NBmNfAtCN>HmpC튶NjHpC(NjL8NBHpC(NjL8NBA텲NNBA텲NNBNHPAc N A텎N&<x*<N JBfNdVHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NBmNfAtCN>HmHmAi>N A텎N&<x*<N JBfNeHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NBmNfACN>ACN>HmAQN pNܬ <r$<H <r$<HHmHmtHtHtHALN AjNN&AjNNDJBfNfN$( valeur approche : HPAN.AjNNN"_NHPN )"_NCN> <"<NAN>N Ndpp@pWBg?<NN\pp@pW?<?<NN\pp@pW?<?<NN\pp@pW?<?<NN\A톴 0N NdpNpNpNpNܸprN <"<N,pNܸpN~pNpNNSoit l'quation (E) : x HP <N"_NHPN( R , a x + b x + c = 0 ( a non nul )"_NCN>prp "<HNp2NN>pNHPN$ = b - 4 a c4"_NCN>prprlNp2NN>N 1er cas : HPpN"_NHPN < 0"_NCN>pN~pNp2r(NAN>pNpAr(NN$(E) n'admet aucune solution N>N$ 2me cas : HPpN"_NHPN = 0"_NCN>pNpPr(NAN>pNp_r(NN(E) admet une seule solutionN>Nx' = xHPp"N"_NHPN = -"_NCN>psrpn"<NpbNN>p{"<NN2aN>pNܬ?<?<q?<?<q~NN$ 3me cas : HPpN"_NHPN > 0"_NCN>pN <r(NAN>pN <r(NN$#(E) admet exactement deux solutions N> <r(NNx' =N>N$- b - (HPpN"_NCN> <rPNAN>?<|?<?<?<?<?<?<?<~N <rlNN2aN>?<P?<?<?<~NpxNHPp"N"_NHPN ="_NCN> <"<NAN>N$- b + HPpN"_NCN> <"<NAN>?<?<?< ?<?<?<?<?<~N <"<NN2aN>?<?<?<?<~NpN~pNpNp<"<@NNCONSEILSN>pNpP"<8NN-N'utilisez les formules queN>p_"<@NN$quand elles s'imposent.4N>px"<8NN-Pensez aux racines videntes.N> <"<8NN$-La forme canonique est parfois4N> <"<@NN$ intressante.aN> <"<8NN-Les formules rduites aussi !N>N NdpC튶NjNpNܬpNpZ"<NNP(x) =N> <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN pN~pxrxNNn'est pas factorisable dans R.N>A텚NzN JBfNzpNpNpNprN <"<N,pNp(rZN <"<&N&pC튶NjHpC(NjL8N JBfNrpC튶NjzN JBfNopN~pNpNp Npn"<NNHUMOUR !N>NrpN~pNpNpNppN~pNpZ"<NNP(x) =N>pNܬ <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN pN~pNܬpC튶NjHpC튶NjL8NBzN\JBfNq4N P(x) = ( x -CN>NqNN P(x) = ( x +CN>px"<NAN>pC튶NjHpC(NjL8NBNHPpC튶NjNPHpC(NjL8NBNHPAi>N <r$<H <r$<HAN.HAN.HA"N HmAoN CA 0HmAoN ANANN ANAN&<x*<N`NrxNp)NN>AN&<x*<N`NrqNp2NN>NzpC튶NjzN JBfNspN~pNpNp Npn"<NNHUMOUR !N>NzpN~pNpNpNppN~pNpZ"<NNP(x) =N>pNܬ <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN pN~pNܬpC튶NjzNVpJBgp/pC튶NjHpC(NjL8N`zNDpJBgp$fNwpx"<NNP(x) =N> <r$<H <r$<HpC튶NjHpC(NjHA"N pC튶NjNNNvHpC(NjNNNvL8N vNXANAN&<x*<N`AHNpC튶NjzN\JBfNu` NuN$( x +CN>pC튶N/pC(Nj _NpC(N/pC튶Nj _NpC튶N/pC(Nj _NpC(N/pC튶Nj _NHx <r$<C튶NHx <r$<C(NAHNrxNAN>pC튶NjNHPpC(NjNPNHPAi>N AHN&<x*<N`H <r$<HAN.HAN.HA"N HmAoN CA 0HmAoN ANANN AN AHN&<x*<N`ANN`NrqNp2NN>NzpC튶NjHpC(NjBL8N JBfNzpN~pNpNpNppN~pNpZ"<NNP(x) =N>pNܬ <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN pN~pNܬpC튶NjHpC튶NjL8NBzN\JBfNyNNP(x) = - ( x -CN>NyjNP(x) = - ( x +CN>px"<NAN>pC튶NjHpC(NjL8NBNHPpC튶NjHpC(NjL8NBNPNHPAi>N <r$<H <r$<HAN.HAN.HA"N HmAoN CA 0HmAoN ANANN ANAN&<x*<N`NrxNp)NN>AN&<x*<N`NrqNp2NN>A텚NzNVJBfNpNpNpNprN <"<N,pNp(rZN <"<&N&pNܸpC튶NjzN JBfN|pN~pNppNܬpNpU"<NNP(x) =N> <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN pN~pN~pNpnrnNN$Il n'y a ici aucune difficult.N> <rnNN&Il vous suffit de mettre x en facteur.N>NpN~pNpNpNppN~pNpZ"<NNP(x) =N>pNܬ <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN pN~pNܬpC튶Nj&<x*<N6HpC(Nj&<x*<N6L8N JBfN pC튶NjHpC(NjL8N JBfN~pN P(x) = ( xCN>AH 00N~pC튶NjHpC(NjL8N`zN JBfN~N P(x) = - ( xCN>AH T0pN~pNpxrxNAN>AHN&<x*<N`AHNNbpxrxNNP(x) =N> <r$<H <r$<HpC튶NjHpC(NjHA"N pC튶NjNNNvHpC(NjNNNvL8N vNXANAN&<x*<N`AHNpC튶NjzN\JBfN AHN&<x*<N`AHNpC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶N/pC(NjHpC(NjL8NB _NpC튶NjANpC튶NjANA{N pC튶NjANA{N A 0 <r$<A NVA NC튶N/AN _NN`NqNqpC튶Nj&<x*<N6HpC튶NjvNXHpC튶NjL8NBL8N\A텾NA텾N&< x*<NVJBfNHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrpr.NXHx. <r$<C틈NNDNpN~pNpNpNpNܬAv 0A텾NN&<x*<N`N&ATN <r$<ATNVATN&<x*<N6A텾NNHATN&<x*<N6A텾NNN&L8N JBfNxCTAv 0AT 0N`zNqpN~pNpNpNAvN&<$x*<NVpJBgp/AvN&<x*<N6A텾NN&<$x*<NVpJBgp$fNHxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNDpr.NXHx. <r$<C틈NN6pC튶NjBNHPp-N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N NAHNrxNp+NN>AHN&<x*<N`AHNAHNH <r$<HAjNHAN.HA"N ANNvHANNvL8N vNXAHNN`&<x*<N`AHNAHNrxNN$) ( xN>AHN&<x*<N`AHNpC튶NjBNHPp+N"_NHPAvNN"_NHPpRN"_NHPAvN&<x*<N6A텾NNN"_NCN>pC튶NjNPNCN>HmHmAi>N HmAQN AjNzNVJBfNAHNrxNp-NN>NAHNrxNp+NN>AHN&<x*<N`AHNAHNH <r$<HAjNHAN.HA"N ANNvHANNvL8N vNXAHNN`&<x*<N`AHNAHNrxNp)NN>NAN*HPp-N"_NJBfNAHNrxNp-NN>AC8N>NHmp"_NC8N>AHNrxNp+NN> pC튶NjNPNCN>HmHmAi>N AN*HPp-N"_NJBfNAHNrxNp-NN>AC8N>NHmp"_NC8N>AHNrxNp+NN> N NdpNpNpNprN <"<N,pNpNpNp!rKN <"<5N&pNpNpNp(rZN <"<&N&pN~pNpNp NpKrdNNSoit le polynome suivant :N>pN~pNpNܬpNpi"<NNP(x) =N> <r$<H <r$<HpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPpC튶NjNHPpC(NjNHPAN N NdpNAPN AN N NdLAN ZLA킈N ZLA킲N ZLA킬N ZLAN ZLANN ZLAHN ZpNܸN\A킲NNpNprNA킲NNܬA킲NN~pNpNpNA킬NNA킈NNANNCHA 0CNA 0AzN CHA 0CNA 0A2NA킲NNܬNCN>HmA "_NJBgNCN>Hmp N"_NpJBgp/AN*HPp0N"_NpJBgp/AN.zN pJBgp$fN2A CN>A2NAzN CHA 0CNA 0ANHPpAN"_NpJBgp/HmpN"_NpJBgp$fNA2NAzN CHA 0CNA 0Hmp-N"_NJBfNHmA "_NJBfNp-NCN>AN/AN"Np-NN>Hmp N"_NpJBgp/Hmp/N"_NpJBgp$fN`ANzN JBfN`AN.zNDJBfN`A2NA 0ANNvvNXANN`ANAN/ <r$<ANN\N"NAN&<x*<N`N/ <r$<ANN\N"N <r$<ANN\ANAN/AN"NAN>Hmp0N"_N pJBgp/Hmp9N"_N pJBgp$fN.ANzN JBfNANNvANN\JBfNHmA"_NCN>AN/AN"NAN>N.ANNvANN\JBfN.HmA"_NCN>AN&<x*<N`ANAN/ <r$<ANN\N"NANNvHANNvL8N vNXANN`&<x*<N`N/ <r$<ANN\N"NAN/AN"NAN>Hmp N"_NJBgPAN.zN JBfNjp1NCN>AN.ANAN.ANA{N AN.ANNANAN.ANNANANANN&<x*<NVpJBgp/HmA "_NpJBgp/Hmp-N"_NpJBgp$fNrA2NAzN CHA 0CNA 0NhA2NANHANHANHANHA"N NzN NdA n0A n0NzpNpNpNprN <"<N,pNܸpN~p NpNp Npr2NN$REMARQUES SUR LES POLYNOMESN>pN~pNpNpNp2rNNJ1 - Vous avez la possibilit d'introduire un polynome de degr au plus 8 .N>pPrNNJ2 - La mthode retenue pour le calcul de P(a) , a rel quelconque , est laN>p_rNN$3 la mthode de HORNER qui est TRS PERFORMANTE .uN>pnrNN@ Pour un calcul approch , choisir l'option 'donne dcimale'N>p}rNN$; Pour une rponse exacte , choisir l'option ' autre '4N>pN~pNpNpN <"<NNExemple : P(x) = xN>pN~pNpNpN <"<N <r$<NN> <r2NN$ a = 1.4144N>pNܬpNpNprN?<?<p?<b?<p?<b?<~NpNpNprN?<b?<?<?<~NpNpNprN <r2NN$a =4N> <r$<H <r$<HNR2HPAHN pNpN?<?<?<&?<?<&?<~NpNpNprN?<&?<?<?<~NpNpNprNpNpN~pNܬ <rN <rN, <rN <rN <rNpNN>NVJfNV/NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp$gppNprN <"<N,pN~p NpNp Npr2NN$CONTRAINTES SUR LES POLYNOMESN>pN~pNpNpNp(r(NN$I- Il n'existe pas de formules pour la rsolution des quations P(x) = 0 ,4N>p7r(NN2 P tant un polynome de degr au moins gal 5 .N>pFr(NNJ- C' est donc vous d'imposer vos contraintes sur P(x) et sur la distanceN>pUr(NN$' entre les ventuelles racines de P(x)PN>pnr2NNP(x) = 0 <==> | P(x) | < eN>pn"<TNN$!Distance minimale entre 2 racines4N> <r$<H <r$<HNe = 0.01HPAN <r$<H <r$<HN$ e = 0.001HPAN <r$<H <r$<HN e = 0.000001HPAN <r$<H <r$<HN$0.1 HPAN <r$<H <r$<HN$0.001HPAN <r$<H <r$<HN$0.00001HPAN <"<NpNN> <"<|NpNN> <r$<H <r$<H <r$<H <r$<HN$O KiHPAxN pN~pNpNpN <"<NN$+L'algorithme de recherche est la DICHOTOMIE4N>NVJfpNNHNvH <r$<L8N\&<x*<N\JBfNjN`NvH <r$<L8N\&<x*<N\JBfN6NV$fN6pNpx"<N <"<N, <"<NpNN>A # =0qN`NvH <r$<L8N\&<x*<N\JBfNNV$fNpNpx"<N <"<N, <"<NpNN>A n0N`NvH <r$<L8N\&<x*<N\JBfNjNV$fNjpNpx"<N <"<N, <"<NpNN>A 'ŬG0NHNvH <r$<L8N\&<x*<N\JBfNzN`NvH <r$<L8N\&<x*<N\JBfNFNV$fNFpNpx"<|N <"<N, <"<|NpNN>A L0N`NvH <r$<L8N\&<x*<N\JBfNNV$fNpNpx"<|N <"<N, <"<|NpNN>A n0N`NvH <r$<L8N\&<x*<N\JBfNzNV$fNzpNpx"<|N <"<N, <"<|NpNN>A 'ŬG0NV/NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp$gPNDN Nd"_A2N LANN ZLAHN ZpNpNpNpNܬAHN/ANN"NAHN&<x*<N`N/ANN&<x*<N`N"N,AHN/ANN"NAHN&<x*<N`N/ANN&<x*<N`N"NAHN&<x*<N`HA2NNvvNXL8N\N/ANN&<x*<N`N"NA2N>N NdNzA$ 0AN AN AN TAN TNDAZN ArN pNpNpNpNpNpr2NpKr7N,pr2Np "<N,pKr2NpM"<N,p"<NpM"<N,A$ 0 <r$<A$NV <r$<A$NN\&<x*<NB&<x*<N`ANNA 0 <r$<A NVA$NA NNB&<x*<N JBfNp1NCN>NpxNCN> <r$<A NN\&<x*<NB&<x*<N`AHNAHNHANNH <r$<H <r$<H <r$<HHmAN ANAN&<x*<NVJBfN`pN~pNpNpNAHN&<x*<N`N/ANN&<x*<N`N"N <r$<ANN\NN>N`\NqN`Nq?<2?<?<9?<ZA"" NpN~pNpNpNpNܬp"<@Np#"<Np "<JNN valider P(x)N>p4"<@NpA"<Np>"<JNN annuler P(x)N>A CN>NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp/NV$fNpNܸp4"<@NpA"<N,p Np4"<@NpA"<N,pNܸArN NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp/NV$fNAN&<x*<N JBfNN$validerCN>NA CN>NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp$fNNHNvH <r$<L8N\&<x*<NN&&<x*<N`A NN`NvH <r$<L8N\&<x*<NN&&<x*<N`A$NA6NA NNDpJBgp/ABNA$NNDpJBgp$fN?<2?<A""N"pNܸ <r$<A NN\&<x*<NB&<x*<N`N/ <r$<A$NN\&<x*<NB&<x*<N`N"N <r$<A NN\&<x*<NB&<x*<N`N/ <r$<A$NN\&<x*<NB&<x*<N`N"N,pNܸC A6 0C$AB 0NV$fNBmA N&<x*<NVpJBgp/A$N&<x*<NVpJBgp$fNNle cofficient de x :CN> <r$<A$NN\&<x*<NBA NN`H <r$<L8N\ANAH C0NN$le terme constant :CN>AH 90pN~pNpNpNN$ Indiquez HPA"_NCN>pnr2NAN>AN gNAN&<x*<NVJBfNpi"<^NANNN>pN~pNpNpNA킲 0BmAHNH <r$<H <r$<H <r$<H <r$<HA5`N AC8N>ACPN>HmARN ACN>HmARN ACN>HmHmAi>N HmAQN AN/AjNC튶NHmAQN AN/AjNC(NHmAoN CA& 0HmAoN A&NANN &<x*<NtJBfN@AN/A8CNAN/APCNNlAN/ACNAN/ACNNzA 0pNp_rN <"<N, <r$<H <r$<HABN NA6NzNDJBfN?<2?<A""N"Bm:BmFANJBg HmN$valider"_NJBgpNܸpNp"<@Np#"<N,pNp"<@Np#"<N,pNܸA C"N>pNprN <"<N, <r$<H <r$<HtHAN pN~AN&<x*< NVJBfN6ND <r$<H <r$<HABN NpNpNpNprN <"<N,pN~pNpNpNp2rdNNSOIT LE POLYNOME SUIVANT :N>ANvNX&<x*<N\H <r$<L8N\AHNpN <r$<AHNN\NrNNAHN&<x*< N\NrzN.pN <r$<AHNN\NrPNAHN&<@x*< N\NrxN.pN~pNpNpN <r$<AHNN\NrdNNP(x) =N>AHN&<x*<N`H <r$<HtHAN N Nd"_AN LATN ZLANN ZLAHN ZLANN ZLAHN ZpNܸAHNNpNANNNAHN/ANN"NAHN&<x*<N`N/ANN&<x*<N`N"N,pNܸATNN~pNpNpNAHN&<x*<N`HANNvvNXL8N\N/ANN&<x*<N`N"NAN>N NdA N TA CN>BmBmBm <r$<A NVA N/p0NCNA N/p1NCNN`NqNqtA튶N8 <r$<A(N8tAdN8 <r$<H <r$<HABN N NdLAN ZLANN ZA N TA&N TpN~pNpNpNpNpNpNܬpNANNrNANN&<x*<N`N"<{N,ANNrNANN&<x*<N`N"<{NANN~pNpNpN <r$<ANNN\N"<DNNconst.N> <r$<ANNN\N"<NpxNN>Bm <r$<A NVA N&<x*<NB&<x*<N`&<x*<N`N/ <r$<ANNN\N"NpxNN>A N&<x*<NB&<x*<N`&<x*<N`N/ <r$<ANNN\N"NA N&<x*<N\NN>N`NqpN~pNpNpNpN~A 0tA NVA N&<x*<NB&<x*<N`N?ANN?A N&<x*<NB&<x*<N`N?ANN&<x*<N`N?~NA NCNHPp0N"_NJBfNA NCNHPAoN CA& 0A NCNHPAoN A N&<x*<N\&<x*<NB&<x*<N`&<x*<N`HA&NANN vNXL8N\AHNA N/A&NANN CdNAHNHANN&<x*<N`HA NCNHPA NCNHPtHtHtHALN N`NqN NdLAN ZLANN ZLAHN ZA N TAN TAN TAN TAZN TANN~ANNܬA 0tA NVA NC튶NjzNDJBfNDA NC튶NjHA NC(NjL8NB&<x*<N JBfN8A NzN JBfNANzN JBfNLAHN/ANN"N <r$<NN>NAHN/ANN"NN$+ 1N> NAHN/ANN"NN$- xN> NANJBfNAHN/ANN"Np+NN> AHNHANNHHmAHN A NCNHPAdTN ACN> AHNHANNHHmA NCNHPtHtHtHALN HmAoN CA 0A NCNHPAoN CA 0 ApN&<x*<NVpJBgp/pCNHPp0N"_NpJBgp$fNNZpCNHPAoN CA 0pCNHPAoN pN~pNpNpNpZ"<NN$P(x) = 4N> <r$<H <r$<HtHAN NNpN~pNpNpNN(mthode de HORNER pour le calcul de P(a)CN>prdNAN>pN~pNpNpNAN&<x*<N`&<x*<NB&<x*<N\AtNAN&<x*<N`&<x*<NBAtNN`ANpNܬAtNr2NAN"<NA 0AN&<x*<N`A NVA N&<x*<NBAtNN`N??<2A N&<x*<NBAtNN`N??<~NN`NqNqAtN??<nAN??<n~NCA 0tA NVAtN&<x*<N`HA NANN\&<x*<NBL8N`AHNA NzN JBfN <r$<AHNN\Nr-NNconst.N>N͜AHNr-NpxNN>A N&<x*<NVJBfN͜pN~pNpNpNAHN&<x*<N`Nr(NA NNN>pN~pNpNpN <"<N <"<N <"<,NN$autre4N>NVJfNHNvH <r$<L8N\&<x*<N\JBfN$N`NvH <r$<L8N\&<x*<N\JBfNϔNV$fNώpNܸ <"<N <"<N,p NpNܸAx 0N$N`NvH <r$<L8N\&<x*<N\JBfN$NV$fN$pNܸ <"<N <"<N,p NpNܸAx 0AxNJBg?<?<?<?<A2" NA 0 <r$<A NV?<A N?A2"N"N`NqNqA C2N>A킬 0AtN"<NN$a =4N>AxN&<x*<N JBfN҄BmpNܬAtN&<x*<N`H <r$<H <r$<H <r$<H <r$<HA5`N AC.N>AC4N>Hm.Hm4Ai>N AC.N>AC4N>Hm.AoN CAH 0Hm4AoN AHNANN AHNAtN&<x*<N`N"<N <"<N,AtN&<x*<N`H <r$<HHm.Hm4tHtHtHALN NAtN&<x*<N`H <r$<H <r$<H <r$< H <r$< HApN CjA킦 0AtN&<x*<N`N??<@AtN&<x*<N`N??<XA&" NAtN&<x*<N`N??<}A&"N"AxN&<x*<N JBfN؎ANC튶NjHANC(NjL8NANCA 0 <r$<A NV <Ѝ/A킦N _NAtN&<x*<N`HA NANN\&<x*<N`&<x*<NBL8N`AHNpNܬpNpNprN <r$<AHNN\N??<s <r$<AHNN\N??<i~NpNpNprNpNܬANNNQlNHANNHPp"_NPHPp*N"_NC,N>N\ANNC,N> AHNrdNA,N> <Ѝ/ <r$<A NN\NC튶NjH <r$<A NN\NC(NjL8N _NAtN&<x*<N`HA NANN\&<x*<N`&<x*<NBL8N`AHNANNNQlN ANNHPp"_NPHPp*N"_NC,N>N4ANNC,N> N`NqAtN"<NAtN&<x*<N`N"<N.AtN"<NNP ( HPAjNN"_NHPN ) ="_NN>pN~pNpNpNAtN&<x*<N`HAjNNNNvvNXL8N`N"<NANNN>pN~pNpNpNNANCNCN>ANCNCN>CA 0 <r$<A NVHmHm.AeN A텎N&<x*<N JBfNtA 0HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLES4HPN OK r"_ NAvNrNޞA퇘CN>HmHm4AeN A텎N&<x*<N JBfNA 0HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNޞA퇘CN>AtN&<x*<N`HA NANN\&<x*<N`&<x*<NBL8N`AHNpNܬpNpNprN <r$<AHNN\N??<s <r$<AHNN\N??<i~NpNpNprNpNܬ <r$<HAN <r$<A NN\NCNHPHmAeN A텎N&<x*<N JBfNA 0HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLES4HPN OK r"_ NAvNrNޞA퇘CN> <r$<A NN\NCNHPHmAeN A텎N&<x*<N JBfNܠA 0HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNޞA퇘CN>HmHmAc N A텎N&<x*<N JBfN@A 0HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNޞAtCN> <r$<A NN\NCNHPHmAeN A텎N&<x*<N JBfNA 0HxN$!PRENEZ DES NOMBRES| |PLUS SIMPLESHPN OK r"_ NAvNrNޞA퇘CN>AtN&<x*<N`HA NANN\&<x*<N`&<x*<NBL8N`NrUNp+NN> <r$<HAN N` <r$<H <r$<HHm.Hm4tHtHtHALN AHN&<x*<N`N"<NN$) =N>pN~A킲 @0pNܬAHN&<x*<N`H <r$<HHmHmtHtHtHALN pNܸ <r$<ANN\NrnNAN"<N.pNܸpNܬpNpNprN?<?<?<?<~NpNpNprNpNܬpN~ <"<NN: multi. par aN> <"<N <"<vNBmA C&N>N NdLANN ZANN TATN TAZN THmARN A텎N&<x*<N JBfN@NACN>HmARN A텎N&<x*<N JBfNNACN>HmAoN CAN 0HmAoN CAT 0HmHmAi>N A텎N&<x*<N JBfNNACN>ACN>HmAoN ANNvvNXANN AZNAZN&<x*<NtJBfNLATNANNN &<x*<NtJBfN~HmAQN AtN&<x*<N`HA NANN\&<x*<N`&<x*<NBL8N`AHNAHN/ANN"NA,N>NFAtN&<x*<N`HATNANNN vNXL8N\HA NANN\&<x*<N`&<x*<NBL8N`AHNAHNHANNHHmHmtHtHtHALN NAtN&<x*<N`HAZNvNXL8N\HA NANN\&<x*<N`&<x*<NBL8N`AHNAHNHANNHHmHmtHtHtHALN N NdAZN AxN TA킦N TAN TBmdBmjpNܸpNpNpNprN <"<N,pNܸ <r$<H <r$<H <r$<HAN pN~pNpNpNpNܸprdNN$RSOLUTION DE P(X) = 0 avec4N>pN~AN&<x*< NVJBfNN <r$<HtHABN N <r$<ANN\vNX&<x*<N\AHNpN~pNpNpN <r$<AHNN\Nr2NNP(x) =N>AHN&<x*<N`H <r$<HtHAN NzANzNVJBfNVpNpZr2N <"<N,pNܬpNpNpZr2N <"<NpN~pNpNpNpirFNN$intervalle de recherche4N>pxrpN~px"<NN( |a-b| < 20 )N>pNpZ"<rN <"<NN,pNܬpZ"<rN <"<NNpN~pi"<NN$ visualisation4N>ps"<N <"<NpN~p}"<NN$oui4N> <"<N <"<N <"<NN$non4N>?<r?<Z?<N?<A " NpNNV$fNN`NvH <r$<L8N\&<x*<N\JBfNNHNvH <r$<L8N\&<x*<N\JBfNpNp}rZN <"<N, <rPN <"<N,AN A` 0NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp$fN?<r?<ZA "N"pNܸps"<N <"<N,pNܸAf 0pNNHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp$fN?<r?<ZA "N"pNܸ <"<N <"<N,pNܸAf 0pNA`N/AfNzNDpJBgp$g:A C N>AfN&<x*<N JBfNNpNpZr2N <"<N,pNܬpNpNpZr2N <"<NpN~pdrdNN$limites de P(x)4N>pN~pirFNpv"<NpsrxNN [ -1 , 1 ]N>p{rFN <"<N <rdNN[ -0.1 , 0.1 ]N> <rFN <"<N <r_NN[ -0.01 , 0.01 ]N>NV/NHNvH <r$<L8N\&<x*<N\pJBgp$fNN`NvH <r$<L8N\&<x*<N\JBfNAx 0pNܸpirFNpv"<N,pNpNܸN`NvH <r$<L8N\&<x*<N\JBfNhAx L0pNܸp{rFN <"<N,pNpNܸN`NvH <r$<L8N\&<x*<N\JBfNAx # =0qpNܸ <rFN <"<N,pNpNܸAxNzNDJBg.pNprN <"<N,pNܬpr2N <"<NNA킦NANN\&<x*< N&<x*<NA톄NAxN&<x*<N&<8<*<NA톊NpNpNprN?<2?<Z?<N?<Z~NANA킦NNBzN\JBfNpNpNprNA킦NA톄NNB&<x*<NB&<x*<N`N??<A킦NA톄NNB&<x*<NB&<x*<N`N??<~NpNpNprNA H0A 0BmpNܬN\ <r$<A NN\&<x*<NA톄NNA킦NN`AHNA$N&<x*<N JBfNpC튶NjHpC(NjL8NHAHN&<x*<N6L8NBHpC튶NjHpC(NjL8NAHNNBL8N`HpC튶NjHpC(NjL8NL8N`ANNNpC튶NjHpC(NjL8NANNA$ 0 <r$<A$NVA$NC튶NjHA$NC(NjL8NHA$NAHNN <rNp-NHPAxNN"_NN>pZrNN$ 0N> <r2NNx = HPA킦NN"_NN> <"<DNANNN>Bg?<#?<?<A2" NA$ 0 <r$<A$NVBgA$N?A2"N"N`NqNqA C2N> <r$<HA0N NPN\pNpZrN <"<N,pNp_r2N <"<NN,pNܬp_r2N <"<NNpN~pirFNN$-La recherche s'opre de la manire suivante :4N>psrZNN<1 - Recherche des intervalles sur lesquels P est strictementN>p}rZNN monotoneN> <rZNN$2 - Utilisation du thorme :sN> <rZNN> f tant une fonction drivable et strictement monotone surN> <rZNN$= [ a , b ] , si f(a)f(b) < 0 il existe une unique solution4N> <rZNN$' sur ] a , b [ l'quation f(x) = 0eN> <rZNN43 - Recherche des ventuelles racines par DICHOTOMIEN> <r$<HA0N A$NzNVJBfNLpN~pNpNpNN$Sur l'intervalle [ nHPA킦NN"_NHPN$ , 4"_NHPANN"_NHPN$ ] , 4"_NCN>A$N&<x*<N JBfNNje ne trouve qu'une racine .CN>NN je trouve HPA$NN"_NHPN racines ."_NCN>A톢N&<x*<N`NrNHmA"_NN>NzNpN~pNpNpNpC튶NjzN JBfNpdr2NN$-Tout rel est solution de l'quation P(x) = 0N>Npdr2NN.Il n'y a aucune solution l'quation P(x) = 0N>NzN Nd <rPNN$a = N>A킬 0N\ <r$<H <r$<H <r$<H <r$< H <r$< HApN CjA킦 0 <rPNN$b =N> <r$<H <r$<H <r$<H <r$<A킦NN\HA킦N&<x*<N`HApN CjA 0pNA킦NANNN|JBfN <rnN <"<N,NA킦NANNVJBfN$AC킦  "002p}rnN <"<N, <rnNA킦NNN> <rnNANNN>NzN NdLANN ZpN~pNpNpNANN"<NN(RECHERCHE L'AIDE DE VOS CONTRAINTES...N>pN~pNpNpNBmXBm(BA킦NC틂NAN TA N T`NLAHN ZpC튶NjHpC(NjL8NHAHN&<x*<N6L8NBHpC튶NjHpC(NjL8NHAHN&<x*<N6L8NBL8N`HpC튶NjHpC(NjL8NHAHN&<x*<N6L8NBL8N`HpC튶NjHpC(NjL8NHAHN&<x*<N6L8NBL8N`N `LAHN ZAHNHAN HpC튶NjHpC(NjL8NHAHN&<x*<N6L8NBL8N`HpC튶NjHpC(NjL8NHAHN&<x*<N6L8NBL8N`HpC튶NjHpC(NjL8NHAHN&<x*<N6L8NBL8N`HpC튶NjHpC(NjL8NAHNNBL8N`HpC튶NjHpC(NjL8NL8N`N `LAHN ZpC튶NjvNXHpC(NjL8NHAHN&<x*<N6L8NBHpC튶Nj&<x*<NBHpC(NjL8NHAHN&<x*<N6L8NBL8N`HpC튶Nj&<x*<NBHpC(NjL8NHAHN&<x*<N6L8NBL8N`HpC튶Nj&<x*<NBHpC(NjL8NHAHN&<x*<N6L8NBL8N`N `LLAHN ZAHNHAN HpC튶NjvNXHpC(NjL8NHAHN&<x*<N6L8NBL8N`HpC튶Nj&<x*<NBHpC(NjL8NHAHN&<x*<N6L8NBL8N`HpC튶NjNPHpC(NjL8NAHNNBL8N`HpC튶NjHpC(NjL8NL8N`N CA 0AN&<n8<*<NVJBfNA n0C킦AH 0AHNHA>N ArNArNzN JBfNB N ArN` N AxNAxNArNNBzN JBfNNBAxNArNNBzNVJBfNATN/ArNNHC|NNBNbATNATN/ANvNXAHNN\C틂NAxCr  "002NBATN&<x*<N`N/ANC틂NpN <rN <"<N,BmATNA NVA NzN JBfNA톖 z@0 NCA톖 0A NC|NjHA NC틂NjHA N&<x*<N`NC틂NjHA톖NHAhN N`ZNqA$NzN JBfN`pNAfN&<x*<N JBfN <rN <"<N,NpPrN <"<N,pN~pNpNpNANNr NN$AAvec vos contraintes et sur cet intervalle , je n'ai rien trouv.N>pN~pNpNpNANN&<x*<N`Nr NNJ - Un conseil : travailler avec un intervalle sur lequel la fonction P estN>ANN&<x*<N`Nr NN$A strictement monotone ( elle est drivable sur R )4N>N NdLA톖N ZLA N ZLAN ZLA톐N ZANHA.N A킈NA NHA.N ANA킈NANN\JBfNBmANA킈NNBzNzJBfNLCA 0C A 0ANHA.N zN pJBgp/A킈NzN pJBgp$fN CAH 0N N ANHA.N zN JBfN CAH 0N ANANN`vNXAHNAHNHA.N A탴NA탴NzN JBfN ,N ANHA.N ANANA탴NNBzN\JBfN CHA 0N CHA 0ANANN\&<8<*<NVJBfN N A톖NAHNN\ANN\JBfN NLCHA 0A$NvNXHA$NvNXN&L8N JBfN A톜 0A$N&<x*<NBANNN`A톢NN A톜 /0A$NzN JBfN pN <r$<ANNN\NrN <"<N,pXNHPA$N&<x*<N`NN"_NHPp N"_NHP <N"_NHPp N"_NCRN>A톜N/A톢N"NHmRAHNN"_NN>A$NpNpNprNpNܬpNܸAfN&<x*<N JBfN2A톐N&<x*<N JBfN A킦NAHNN\A톄NNB&<x*<NB&<x*<N`N??<PA킦NAHNN\A톄NNB&<x*<NB&<x*<N`N??<D~NN2A킦NAHNN\A톄NNB&<x*<NB&<x*<N`N??<PA킦NAHNN\A톄NNB&<x*<NB&<x*<N`N??<D~NpNpNprNpNܸp NN Ndpp@pWBg?<NN\pp@pW?<?<NN\pp@pW?<?<NN\pp@pW?<?<NN\A톴 @0N NdA!N ANHAN N NdAN TAN TAN&<x*<N JBfNhAN&<x*<N6HA킦NvNXA"NNBL8N\A텚NA텚NBHA킦NvNXL8NANAN&<8<*<NBANNBANN\N&ANA2NN\pNܬpNN`ANrpNpNprNBgAN??<AN?~NANANN\HAN&<8<*<NBL8NANNm HP <N"_NHPp N"_NHPANN"_NCN> <r$<ANN\Nr NAN>pNܬp NAN&<x*<N6HA킦NvNXHANA"NN\L8NBL8N\A텚NpNpNprNANANN\zN JBfNANBHA킦NNPL8NANpNNx' = xHPp"N"_NHPp N"_NHP <N"_NHPp N"_NHPANN"_NCN>AN&<x*<N`N"<NAN>A*N&<x*<NBANNBA$NN`ANAN?AN?AN?AN?~NNA텚NzNVJBfNPANBHA텚NNL8N\HA킦NNPL8NANANBHA텚NNL8N`HA킦NNPL8NANpNN$x' HP <N"_NHPp N"_NHPANN"_NCN>pxNHPp"N"_NHPp N"_NHP <N"_NHPp N"_NHPANN"_NCN>A*N&<x*<NBANNBA$NN`ANAN?AN?AN?AN?~NA*N&<x*<NBANNBA$NN`ANAN?AN?AN?AN?~N <r$<ANN\N"<NAN>AN&<x*<N`N"<NAN>N <r$<ANN\N"<NN$aucune solutionN>N`NvANNN|JBfNNXN`ANrA2NANANN\HAN&<8<*<NBL8NANpNNm HP <N"_NHPp N"_NHPANN"_NCN> <r$<ANN\Nr NAN>pNܬpNpNprNBgAN??<AN?~NpNpNprNpNܬp NAN&<x*<N6HA킦NvNXHANA"NN\L8NBL8N\A텚NANANN\zN JBfNpNANBHA킦NNPL8NANNx' = xHPp"N"_NHPp N"_NHP <N"_NHPp N"_NHPANN"_NCN>AN&<x*<N`N"<NAN>A*N&<x*<NBANNBA$NN`ANAN?AN?AN?AN?~NNXA텚NzNVJBfNANBHA텚NNL8N\HA킦NNPL8NANANBHA텚NNL8N`HA킦NNPL8NANpNN$x' HP <N"_NHPp N"_NHPANN"_NCN>pxNHPp"N"_NHPp N"_NHP <N"_NHPp N"_NHPANN"_NCN>A*N&<x*<NBANNBA$NN`ANAN?AN?AN?AN?~NA*N&<x*<NBANNBA$NN`ANAN?AN?AN?AN?~N <r$<ANN\N"<NAN>AN&<x*<N`N"<NAN>NX <r$<ANN\N"<NN$aucune solutionN>NV$g2NA2NN\pNܬpNN`ANrpNpNprNBgAN??<AN?~NANANN\HAN&<8<*<NBL8NANNm HP <N"_NHPp N"_NHPANN"_NCN> <r$<ANN\Nr NAN>N`NvANNDJBfNzN`ANrA2NBgAN??<AN?~NANANN\HAN&<8<*<NBL8NANNm HP <N"_NHPp N"_NHPANN"_NCN> <r$<ANN\Nr NAN>NV$gp NpNpNprNN NdLAN ZA N TA$N TpNpNpNܬBmA 0BmA$NA NN\&<x*<NA*NNAHNA$N&<x*<N JBfNpC튶NjHpC(NjL8NHAHN&<x*<N6L8NBHpC튶NjHpC(NjL8NAHNNBL8N`HpC튶NjHpC(NjL8NL8N`ANNNpC튶NjHpC(NjL8NANNA$ 0 <r$<A$NVA$NC튶NjHA$NC(NjL8NHA$NAHNNNVJfpNpNpNܬNHA$NrN`ANrA$NzNVpJBgp/A$N&<x*< N\pJBgp/ANzNVpJBgp/AN&<x*<N\pJBgp$fN#BgAN??<AN?~NA$N?BgA$N??<~NpN0N#pN0NHA$NrN`ANrNHNvHA$NL8N\zNpJBgp/N`NvHANL8N\zNpJBgp$fN$N$ANA$NzNVpJBgp/A$N&<x*< N\pJBgp/ANzNVpJBgp/AN&<x*<N\pJBgp$fN$BgAN??<AN?~NA$N?BgA$N??<~NpN0N$pN0NV/AN&<x*<N\pJBgp$grprN <"<N,BgAN??<AN?~NA$N?BgA$N??<~NN\ANNzpNNVJfpNܸpN <"<NN$)Choisissez l'unit sur l'axe (Ox) (en cm)N>A*>N CpN~p"<,NAN>Bm:pN~pN <"<NN$)Choisissez l'unit sur l'axe (Oy) (en cm)4N>A*>N CN NdA/BN A CN>Bm|NHNvH <r$<L8N\&<x*<N\pJBgp/N`NvH <r$<L8N\&<x*<N\pJBgp$fN-BNHNvH <r$<L8N\&<x*<NN&&<x*<N`A NN`NvH <r$<L8N\&<x*<NN&&<x*<N`A$NA6NA NNDpJBgp/ABNA$NNDpJBgp$fN,?<2?<A""N" <r$<A 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information-------------123456sys_N_P un peu de cours donne d'un systme de n quations p inconnues ATARI rsout votre dmarche rappel du systme recommencer la rsolution du systme 2_degr un peu de cours formules donne d'un polynome du 2_nd degr rsolution algbrique de P(x) = 0 P(x) > 0 P(x) < 0 P(x) >= 0 P(x) <= 0 factorisation rsolution algbrique de P(x) = m minimum ou maximum de P(x) polynome remarques et contraintes sur P(x) donne d'un polynome quelconque rsolution de P(x) = 0 graphe courbe d'quation y = P(x) ancien graphique + courbe y = P(x) impression du graphique rsolution graphique de P(x) = m conserver le graphique rappeler le graphique aide crire un nombre avec ATARI conserver la page texte rappeler la page texte calcul de P(a) avec a = ? effacer STOP quitter le programme ***0.512345678910autre333333333333000000000000444444444444Li->aLiLi->Li<->LjCi<->CjPivot hPivot bArretCours1R^l"x@x \  B \ N \"  $( L    r: J` h<~~ &Vd:Jfd$ ؖ~(z"D(zR(z^(X(zj(z(z" D h~.DJJ8D(^ @( Rv\J (D:  ,F\ 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