Question

If1/2 is a zero of p(x)=2x^4-ax^3+4x^2+2x+1. Find the value of a

Answer 1

Answer :

$\rule{100}2$

Since 1/2 is a zero of the given polynomial then remainder must be zero.

$\sf P(x)=2x^4 - ax^3+4x^2+2x+1$

Substitute x = 1/2.

$\sf P(\dfrac{1}{2}) = 2(\dfrac{1}{2})^4 - a(\dfrac{1}{2})^3 + 4(\dfrac{1}{3})^2+2(\dfrac{1}{2})+1=0$

$\sf\implies \dfrac{1}{8}-\dfrac{a}{8}+1+1+1=0$

$\sf\implies \dfrac{1}{8}+3 =\dfrac{a}{8}=0$

$\sf\implies \dfrac{25}{8}=\dfrac{a}{8}$

$\sf\therefore a = 25$

Answer : The value of ' a ' is 25.

$\rule{200}2$