Question

6. Find the value of k, if 2x + 1 is a factor of
(3k + 2) x^3 + (k-1).​

Answer 1

Let take f(x)=(3k+2)x 3 +(k–1)

Now, 2x+1=0

x=−1/2

As, 2x+1 is a factor of f(x) then the remainder should be 0

f(−1/2)=(3k+2)(−1/2) 3+(k–1)=0

∴(3k+2)( 2−1) 3+(k−1)=0

⇒ 8−(3k+2)+(k−1)=0

⇒ 8−3k−2+8k−8=0

⇒5k−10=0

5k=10=0k=2