Question

Find K if 4 x square - 2 X square + kx + 5 leaves a remainder -10 when divided by 2x+1​

Answer 1

Answer:

$k = 31$

Step-by-step explanation:

Given

$f(x) = 4x^2 - 2x^2 + kx + 5$

$r = -10$ --- remainder

$d = 2x + 1$ --- divisor

Required

Find k

We have:

$d = 2x + 1$ --- divisor

Equate to 0

$2x + 1 = 0$

Solve for x

$2x = -1$

$x =-0.5$

This means that:

$f(-0.5)=-10$

So, we have:

$4*(-0.5)^2 - 2*(-0.5)^2 + k*-0.5 + 5 =-10$

$0.5 -0.5k + 5 =-10$

Collect like terms

$-0.5k=-10-5-0.5$

$-0.5k=-15.5$

Solve for k

$k = -15.5/-0.5$

$k = 31$