# How do you factor #x^2 -x+7#?

##### 1 Answer

Feb 22, 2016

Use the quadratic formula to find:

#x^2-x+7 = (x-1/2-(3sqrt(3))/2 i)(x-1/2+(3sqrt(3))/2 i)#

#### Explanation:

This has discriminant

#Delta = b^2-4ac = (-1)^2-(4*1*7) = 1-28 = -27#

Since this is negative

The roots of

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

#= (-b+-sqrt(Delta))/(2a)#

#= (1+-sqrt(-27))/2#

#= 1/2 +- sqrt(27)/2 i#

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

Hence

#x^2-x+7 = (x-1/2-(3sqrt(3))/2 i)(x-1/2+(3sqrt(3))/2 i)#