# What is the discriminant of #x^2+x+1=0# and what does that mean?

##### 1 Answer

Jul 16, 2015

The discriminant is -3. It tells you that there are no real roots, but there are two complex roots to the equation.

#### Explanation:

If you have a quadratic equation of the form

The solution is

The discriminant

The discriminant "discriminates" the nature of the roots.

There are three possibilities.

- If
#Δ > 0# , there are**two separate**real roots. - If
#Δ = 0# , there are**two identical**real roots. - If
#Δ <0# , there are**no**real roots, but there are two complex roots.

Your equation is

This tells you that there are no real roots, but there are two complex roots.

We can see this if we solve the equation.