If x = –1/2 is a zero of the polynomial p (x) = 8x³ – ax² – x + 2, find the value of a.

Concept Used:

If x = a is a root of a polynomial f(x), then f(a) = 0

Explanation:

We have,

p (x) = 8x³ – ax² – x + 2

Put x = – 1/2

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

Given that,

x = – 1/2 is a root of p (x)

p (– 1/2 ) = 0

Therefore,

a = 6