# What is the discriminant of #x^2-4x+4=0# and what does that mean?

##### 2 Answers

The discriminant is zero. It tells you that there are two identical real 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 two identical real roots.

We can see this if we solve the equation by factoring.

There are two identical real roots to the equation.

The discriminant

#### Explanation:

The discriminant

1] If the discriminant is positive you'll have 2 separate real solutions

2] If the discriminant is equal to zero you'll have 2 coincident real solutions,

3] If the discriminant is negative you'll have two complex solutions (in this case, at least for now, you stop and say that there will not be REAL solutions).

The discriminant is given as:

so:

and

So you have case 2] two coincident solutions (if you solve your equation you'll find that it is satisfied by