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Question Number 50445 by ANTARES VY last updated on 16/Dec/18
TherootsofthefallowingfunctionsaretheSequencesofarithmeticprogressiyonf(x)=x5−20x4+ax3+bx2+cx+24f(8)=?
Commented by tanmay.chaudhury50@gmail.com last updated on 16/Dec/18
plscheckthequestion..iff(x)=0valueofxisintermsofa,b,csof(8)=85−20×84+a×83+b×82+c×8+24
Answered by ajfour last updated on 16/Dec/18
letrootsbexi=p−2q,p−q,p,p+q,p+2q⇒Σxi=5p=20⇒p=4Πxi=p(p2−q2)(p2−4q2)=−24letq2=s⇒(16−s)(16−4s)+6=04s2−80s+262=0or2s2−40s+131=0s=q2=10±1382(notaconvinientvalue..)a=Σx1x2b=−Σx1x2x3c=Σx1x2x3x4f(8)=85−20(8)4+a(8)3+b(8)2+8c+24
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