A quartic polynomial is given by P(x)=x^ 4 +px^ 3 +qx^ 2 +rx+s

MATHEMATICS · Multi-part · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables

Problem

A quartic polynomial is given by

P(x)=x^{4}+px^{3}+qx^{2}+rx+s,

where

p,q,r,s\in\mathbb{R}

. The following information is known:

P(1)=0,\; P(-1)=0,\; P(2)=3

and

P(-3)=-5

. (i) Form four separate equations in

p, q, r, s

using the above conditions. (ii) Solve the system to find the values of

p, q, r,

and

s

. (iii) Hence write the complete polynomial

P(x)