# What is the discriminant of #2x^2 + 5x + 5 = 0# and what does that mean?

##### 1 Answer

#### Answer:

For this quadratic, **no** real solutions, but it does have **two** distinct complex ones.

#### Explanation:

The general form for a quadratic equation is

The general form of the **discriminant** looks like this

Your equation looks like this

which means that you have

The discriminant will thus be equal to

The two solutions for a general quadratic are

When **no real solutions**, since you're extracting the square root from a *negative number*.

However, it does have two distinct **complex solutions** that have the general form

In your case, these solutions are