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Given-f-x-x-5-ax-4-bx-3-cx-2-dx-c-and-f-1-f-2-f-3-f-4-f-5-Find-a-

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Question Number 188651 by cortano12 last updated on 04/Mar/23
Given f(x)=x^5 +ax^4 +bx^3 +cx^2 +dx+c and f(1)=f(2)=f(3)=f(4)=f(5). Find a.
Givenf(x)=x5+ax4+bx3+cx2+dx+candf(1)=f(2)=f(3)=f(4)=f(5).Finda.
Answered by horsebrand11 last updated on 04/Mar/23
f(x)=(x−1)(x−2)(x−3)(x−4)(x−5)+p f(x)=x^5 −15x^4 +85x^3 −225x^2 +274x−120+p ⇒a=−15, b=85 , c=−225, d=274, ⇒−225=−120+p ⇒p=−105 ∴ f(x)=(x−1)(x−2)(x−3)(x−4)(x−5)−105
f(x)=(x−1)(x−2)(x−3)(x−4)(x−5)+pf(x)=x5−15x4+85x3−225x2+274x−120+p⇒a=−15,b=85,c=−225,d=274,⇒−225=−120+p⇒p=−105∴f(x)=(x−1)(x−2)(x−3)(x−4)(x−5)−105

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