Question

find the value of K for which (2x-1) is factor of (2x^3+kx^2+11x+k+3)​

Answer 1

Answer:

2x-1 is a factor

x=1/2

on putting value in given equation we get

5K+35=0

5k=-35

k=-35/7

k=-5

Answer 2

Hey... here's your answer.

Answer:

K = 55

Step-by-step explanation:

$p(x) = 2 {x}^{3} + k {x}^{2} + 11x + k + 3$

put 2x+1 = 0

$2x = - 1 \\ x = \frac{ - 1}{2}$

put the value of x in p(x)

Since, 2x+1 is a factor of p(x).

$p( \frac{ - 1}{2} ) = 0 \\ 2( \frac{ - 1}{2} ) ^{3} + k( \frac{ - 1}{2} ) ^{2} + 11( \frac{ - 1}{2} ) + k + 3 = 0 \\ \frac{ - 2}{8} + \frac{k}{4} - \frac{ - 11}{2} + k + 3 = 0 \\ \frac{ - 1}{2} - \frac{11}{2} + 3 + \frac{k}{4} + k = 0 \\ \frac{ - 11}{4} + \frac{5k}{4} = 0 \\ \frac{5k}{4} = \frac{11}{4} \\ 5k = \frac{11}{4} \times 4 \\ k = 11 \times 5 \\ k = 55$

Hope this will help you.