Question

For what value of k is 2x3 + 10x2 + 11x k + 3 exactly divisible by 2x – 1?

Answer 1

f(x) = 2x³ + 10x² + 11kx + 3 

Given that (2x - 1) is a factor. 

Then, 

$f\bigl( \frac{1}{2} \bigr ) = 2 \bigl(\frac{1}{2}\bigr)^3 + 10 \bigr( \frac{1}{2}\bigr )^2 + \frac{11k}{2} + 3 = 0$

⇒ $\frac{1}{4}+ \frac{10}{4} + \frac{22k}{4} + \frac{12}{4} = 0$

⇒ $22 k = -23$

⇒ $k = \frac{-23}{22}$

Answer 2

Hey buddy..
Have a look at the picture

Hope it's helpful for you