# How do you find all the real and complex roots of #x^3 + 8 = 0#?

##### 1 Answer

Jan 19, 2016

#### Explanation:

Split this apart using the sum of cubes identity.

#(x+2)(x^2-2x+4)=0#

Now, you know that either

#x+2=0color(white)(xxxx)"or"color(white)(xxxx)x^2-2x+4=0#

Solving the first of these gives that

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

#x=(2+-sqrt(4-16))/2=(2+-2sqrt3i)/2=1+-sqrt3i#