I need help with the foll. problem:

P(x) = x^{3}+ 2x^{2}- (4K + 5)x - 6 have three distinct zeros. Two of these are identical to the zeros of f(x) = x^{2}+ 5x + K. Compute the value of K.

Attempts:Using the rational roots theorem:

+-1, +-2, +-3, +-6

I chose -3 because i thought it would work. Then I used synthetic division to find the other zeros.

-3 1 2 (4K + 5) -6

-3 3 6

1 -1-20

(4k+5) must be-5because -5+3 =-2

next I found the other zeros:

(x^{2}- x - 2) = (x + 1) (x - 2)

So, the zeros of this function are: 2, -1, and -3. As stated before, (4K + 5) = - 5

4k + 5 = -5

k = - 10/4 or -2.5

Now, when I substitute -2.5 to f(x) = x^{2}+ 5x + K, the zeros i get are not the same to the other function...I'm stuck here.

Thanks for helping me