# What is the discriminant of #3x^2 + 6x + 5# and what does that mean?

##### 1 Answer

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

#### Explanation:

For a quadratic equation written in general form

the **discriminant** is defined as

In your case, the quadratic looks like this

which means that you have

The discriminant will thus be equal to

When **no real solutions**. It does have two *distinct* complex solutions derived from the general form

which in this case becomes

In your case, these two solutions are