How to use the discriminant to find out what type of solutions the equation has for m^2 + m + 1 = 0?

1 Answer
May 17, 2015

m^2+m+1 is of the form am^2+bm+c with a=b=c=1.

The discriminant is given by the formula:

Delta = b^2-4ac = 1^2 - (4xx1xx1) = 1-4 = -3

Delta < 0 so there are no real roots. There are two distinct complex roots.

As a matter of interest, the two roots are omega and omega^2, where

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

is called the primitive cube root of unity.

Another way of expressing it is:

omega = cos((2pi)/3)+isin((2pi)/3) = e^((2pi)/3i)