Question

If the polynomial $f(x)=2x^3-kx^2+5x+9$ is exactly divisible by x+2, then, k =

• A. 17/4
• B. -17/4
• C. -15/4
• D. 15/4

Answer 1

Answer:

B. -17/4

we have,

$f(x)=2x^3-kx^2+5x+9$ is exactly divisible by x+2

x=-2 will be a root

f(-2)=0

$2(-2)^3-kx(-2)^2+5(-2)+9=0$

$2(-8)-kx(4)-10+9=0$

-16-4k-1=0

-17-4k=0

4k=-17

k=-17/4