# How do you solve using the quadratic formula: # x^2+x+1=0#?

##### 1 Answer

Nov 20, 2015

See explanation...

#### Explanation:

This has zeros given by the quadratic formula:

#x = (-b+-sqrt(b^2-4ac))/(2a) = (-1+-sqrt(1^2-(4xx1xx1)))/(2xx1)#

#=(-1+-sqrt(1-4))/2 = (-1+-sqrt(-3))/2 = (-1+-sqrt(3)i)/2#

#= -1/2+-sqrt(3)/2i#

The number

is called the primitive Complex cube root of unity and is used extensively when solving cubic equations.

#omega^2 = bar(omega) = -1/2-sqrt(3)/2i#

#omega^3 = 1#