Question

Dtermine the value of K such that -2 is cone root of the equation 2x^3+(K+1)x^2=4-x^2

I tried it a couple of times and I keep getting the wrong answer. The answer is K=3.

Answer 1

If x = -2 is a root, then
2(-2)^3 + (k+1)(-2)^2 = 4 - (-2)^2
-16 + (k+1)(4) = 4 - 4
4(k+1) = 16
k+1 = 4
k = 3

the most likely error you made probably is in the
(-2)^3 = -8
or
- (-2)^2
= -(4)
= -4