If x = −1/2 is zero of the polynomial p(x)

Question:
If $x=-1 / 2$ is zero of the polynomial $p(x)=8 x^{3}-a x^{2}-x+2$, Find the value of a

Solution:

We know that, $p(x)=8 x^{3}-a x^{2}-x+2$

Given that the value of x = -1/2

Substitute the value of x in f(x)

$p(-1 / 2)=8(-1 / 2)^{3}-a(-1 / 2)^{2}-(-1 / 2)+2$

= - 8(1/8) - a(1/4) + 1/2 + 2

= -1 - (a/4 + 1/2 + 2)

= 1 - (a/4 + 1/2)

= 3/2 − a/4

To, find the value of a, equate p(-1/2) to zero

p(-1/2) = 0

3/2 - a/4 = 0

On taking L.C.M

$\frac{6-a}{4}=0$

$\Rightarrow 6-a=0$

$\Rightarrow a=6$