If x = -1/2 is a zero of the polynomial p ( x ) = 8 x 3 - ax 2 - x + 2, find the value of a .

Question

If x = -1/2  is a zero of the polynomial p ( x ) = 8 x 3  -  ax 2  -  x  + 2, find the value of a .

Philoid · Accepted Answer

We have,

p (x) = 8x³- ax²- x + 2

Put x = -1/2

p (-1/2) = 8 (-1/2)² – a (-1/2)² – (-1/2) + 2

= 8 * – a * + + 2

= -1 - + + 2

= -

Given that,

x = -1/2 is a root of p (x)

p (-1/2) = 0

Therefore,

- = 0

=

2a = 12

a = 12/2 = 6