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