Question

If 2x - 1 is a factor of 4x^3 - 16x^2 + 10x + k then find the value of k

Answer 1

Given f(x) = 4x^3 - 16x^2 + 10x + k.

Given 2x - 1 is a factor of f(x).

By factor theorem,

f(1/2) = 0.

= > f(1/2) = 4(1/2)^3 - 16(1/2)^2 + 10(1/2) + k = 0

               = 4(1/8) - 4 + 5 + k = 0

               = 1/2 + 1 + k = 0

               = 3/2 + k = 0

               = k = -3/2.



Therefore the value of k = -3/2.



Hope this helps!

Answer 2

SOLUTION:-
GIEVN BY EQUASTION IS:-

$p(x) = 4 {x}^{3} - 16 {x}^{2} + 10x +k$
(2x-1) is factor of given equation then,
we get ,
$x = \frac{1}{2}$
$now \\ p( \frac{1}{2} ) = 4x^3 - 16x^2 + 10x + k = 0 \\ 4 \times {( \frac{1}{2}) }^{3} - 16 \times { (\frac{1}{2} )}^{2} + 10 \times \frac{1}{2} + k = 0 \\ 4 \times \frac{1}{8} - 16 \times \frac{1}{4} + 5 + k = 0 \\ \frac{1}{2} - 4 + 5 + k = 0 \\ \frac{1}{2} + 1 + k = 0 \\ k = - (\frac{1 + 2}{2} ) \\ k = - \frac{3}{2}$
hence , k = - \frac{3}{2}

■I HOPE ITS HELP■