Question

if 1/2 is zero of the polynomial p(x)=8x^3+ax^2-4x+2​

Answer 1

Answer :

a = - 4

Explanation:

If 1/2 is a zero of the above p(x). On substituting it back in the equation would give zero as a solution of all calculations

Given Polynomial,

$\sf \: p(x) = {8x}^{3} + a {x}^{2} - 4x + 2$

To finD

Value of a

Now,

$\sf \: p( \dfrac{1}{2} ) = 8( \dfrac{1}{2}) {}^{3} + a (\dfrac{1}{2} ) {}^{2} - 4 \times \dfrac{1}{2} + 2 \\ \\ \longrightarrow \: \sf \: \: 0 = 8 \times \dfrac{1}{8} + \dfrac{a}{4} - \cancel{2} \: + \cancel{2} \\ \\ \longrightarrow \: \sf \: \dfrac{a}{4} = - 1 \\ \\ \longrightarrow \: \underline{ \boxed{\sf {a = - 4}}}$