Question and Answers Forum

All Questions      Topic List

Relation and Functions Questions

Previous in All Question      Next in All Question      

Previous in Relation and Functions      Next in Relation and Functions      

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.

$$\:\:\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{5}} +\mathrm{ax}^{\mathrm{4}} +\mathrm{bx}^{\mathrm{3}} +\mathrm{cx}^{\mathrm{2}} +\mathrm{dx}+\mathrm{c} \\ $$$$\:\mathrm{and}\:\mathrm{f}\left(\mathrm{1}\right)=\mathrm{f}\left(\mathrm{2}\right)=\mathrm{f}\left(\mathrm{3}\right)=\mathrm{f}\left(\mathrm{4}\right)=\mathrm{f}\left(\mathrm{5}\right). \\ $$$$\:\mathrm{Find}\:\mathrm{a}. \\ $$

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

$$\:{f}\left({x}\right)=\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left({x}−\mathrm{3}\right)\left({x}−\mathrm{4}\right)\left({x}−\mathrm{5}\right)+{p} \\ $$$$\:{f}\left({x}\right)={x}^{\mathrm{5}} −\mathrm{15}{x}^{\mathrm{4}} +\mathrm{85}{x}^{\mathrm{3}} −\mathrm{225}{x}^{\mathrm{2}} +\mathrm{274}{x}−\mathrm{120}+{p} \\ $$$$\Rightarrow{a}=−\mathrm{15},\:{b}=\mathrm{85}\:,\:{c}=−\mathrm{225},\:{d}=\mathrm{274},\: \\ $$$$\Rightarrow−\mathrm{225}=−\mathrm{120}+{p} \\ $$$$\Rightarrow{p}=−\mathrm{105} \\ $$$$\therefore\:{f}\left({x}\right)=\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left({x}−\mathrm{3}\right)\left({x}−\mathrm{4}\right)\left({x}−\mathrm{5}\right)−\mathrm{105} \\ $$$$ \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com