Question

If $2$ is a zero of the polynomial $p\left(x\right)=2x^2-3x+7a$, find the value of $a$

Answer 1

Given polynomial $p\left(x\right)=2x^2-3x+7a$ is zero polynomial if x is 2

Replace x by 2 we get

$\therefore 2(2{)}^2-3(2)+7a=0$

$\Rightarrow 2\times 4-3\times 2+7a=0$

$\Rightarrow 8-6+7a=0$

$\Rightarrow 2+7a=0$

Add -2 both sides we get

$2+7a-2=0-2$

$\Rightarrow 7a=-2$

Divided by 7 both side we get

$a=-\frac{2}{7}$

So $a=-\frac{2}{7}$