What are the roots of x^3 + 9 x^2 + 6x -16 ?

To find the roots of x^3+9x^2+6x-16 =
0

The sum of the coefficients , 1+9+6-16 =
0.

Therefore x= 1 is a root.

So x-1 is
a factor.

Therefore x^3+9x^2+6x-16 =
(x-1)(x^2+kx+16)

We equate the coefficients of x on both
sides:

6= 16-k.

 So k = 16-6 =
10.

Or k = 10

Therefore  x^2+kx+16 =
x^2+10x+16 = (x+8)(x+2).

So x^3+9x^2+6x-16 = 0 =
(x-1)(x+8)(x+2).

So the other roots are given by x+8 = 0, or x+2 =
0.

x+8 = 0 gives x= -8.

x+2 = 0 gives
x= -2.

So the x =1, x=-8 and x= -2 are the roots of the given
equation.