# How do you find all the real and complex roots of #x^3 + 9x^2 + 19x - 29 = 0#?

##### 1 Answer

Jan 22, 2016

#### Explanation:

The potential real roots of a polynomial are the factors of

Since

Use synthetic division or polynomial long division to find that

#(x^3+9x^2+19x-29)/(x-1)=x^2+10x+29#

The other two roots can be found through applying the quadratic formula on

#x=(-b+-sqrt(b^2-4ac))/(2a)=(-10+-sqrt(-16))/2=color(red)(-5+-2i#