*Answer :*

**Concept Used:**

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

Explanation:

We have,

*p* (*x*) = 8*x*^{3} – *ax*^{2} – *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**

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