If `x=1/2` is a zero of the polynomial `f(x)=8x^3+a x^2-4x+2,`find the value of `a`

Explanation

To find the value of \( a \) such that \( x = \frac{1}{2} \) is a zero of the polynomial \( f(x) = 8x^3 + ax^2 - 4x + 2 \), we will follow these steps:

### Step 1: Substitute \( x = \frac{1}{2} \) into the polynomial
We start by substituting \( x = \frac{1}{2} \) into the polynomial \( f(x) \).

\[ f\left(\frac{1}{2}\right) = 8\left(\frac{1}{2}\right)^3 + a\left(\frac{1}{2}\right)^2 - 4\left(\frac{1}{2}\right) + 2 \]
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