Question

find 'k' if
$4x^{3} - 2x^{2} + kx + 5$
leaves a remainder -10 when divided by
$2x - 1.$

Answer 1

Given Equation is f(x) = 4x^3 - 2x^2 + kx + 5.

According to remainder theorem,

2x - 1 = 0

2x = 1

x = 1/2.

Plug x = 1/2 leaving a remainder -10, we get

f(1/2) = 4(1/2)^3 - 2(1/2)^2 + k(1/2) + 5 = -10

           4(1/8) - 2(1/4) + k(1/2) + 5 = -10

           1/2 - 1/2 + k/2 + 5 = -10

           k/2 + 5 = -10

           k/2 = -15

           k = -30.


Therefore the value of k = -30.


Hope this helps!

Answer 2

HELLO DEAR,

4x³-2x²+kx+5=0
and, given,
x =1/2

4(1/2)³-2(1/2)²+k(1/2)+5=-10

4×1/8-2×1/4+k/2+5=-10

1/2-1/2+k/2+5=-10

k/2=-10-5
k/2=-15

k=-30
I HOPE ITS HELP YOU DEAR,
THANKS