# How do you find all the real and complex roots of #x^3 - 2x^2 + 10x + 136 =0#?

##### 1 Answer

#### Explanation:

We should first try to find a real root of the polynomial. Any real root, since the coefficient of the high highest degree term is

Thus, our potential factors are

Attempt synthetic division or polynomial long division with the factors until you find one that doesn't give a remainder.

The only factor that will work is

We can determine the other two roots by dividing the original function and

#(x^3-2x^2+10x+136)/(x+4)=x^2-6x+34#

To determine the remaining two roots, we can apply the quadratic formula to

#x=(-b+-sqrt(b^2-4ac))/(2a)=(6+-sqrt(-100))/2=color(red)(3+-5i#

The graph should have one real root at

graph{x^3-2x^2+10x+136 [-15, 15, -2000, 2000]}