Question

If 2x – 1 is a factor of 4x3 – 16x2 + 10x + k, then find the value of k.

Answer 1

Given Factor = 2x - 1

=> 2x - 1 = 0

=> 2x = 1

=> x = 1 / 2 = 0.5

Therefore f ( x ) = 0.5

Substituting in the equation we get,

Equation : 4x³ - 16x² + 10x + k

=> 4 ( 0.5 )³ - 16 ( 0.5 )² + 10 ( 0.5 ) + k = 0

=> 4 ( 0.125 ) - 16 ( 0.25 ) + 5 + k = 0

=> 0.5 - 4 + 5 + k = 0

=> 1 + 0.5 + k = 0

=> 1.5 + k = 0

=> k = - 1.5

Therefore the value of ' k ' is equal to ( - 3 / 2 ) or - 1.5.