# How do you describe the nature of the roots of the equation #x^2-4x+4=0#?

##### 1 Answer

We can factor the expression on the right as:

Therefore the two roots for this quadratic are the same:

#### Explanation:

We can also use the discriminate to show this same result:

The quadratic formula states:

For

The discriminate is the portion of the quadratic equation within the radical:

If the discriminate is:

- Positive, you will get two real solutions

- Zero you get just ONE solution

- Negative you get complex solutions

To find the discriminant for this problem substitute:

Because the discriminate is