# Discriminant review

CCSS Math: HSA.REI.B.4, HSA.REI.B.4b

The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.

### Quick review of the quadratic formula

The quadratic formula says that

for any quadratic equation like:

## What is the discriminant?

The $\goldD{\text{discriminant}}$ is the part of the quadratic formula under the square root.

The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation.

- A
**positive**discriminant indicates that the quadratic has**two distinct real number solutions**. - A discriminant of
**zero**indicates that the quadratic has a**repeated real number solution**. - A
**negative**discriminant indicates that**neither of the solutions are real numbers**.

*Want to understand these rules at a deeper level? Check out this video.*

### Example

We're given a quadratic equation and asked how many solutions it has:

From the equation, we see:

- $a=6$
- $b=10$
- $c=-1$

Plugging these values into the discriminant, we get:

This is a positive number, so the quadratic has two solutions.

This makes sense if we think about the corresponding graph.

Notice how it crosses the $x$-axis at two points. In other words, there are two solutions that have a $y$-value of $0$, so there must be two solutions to our original equation: $6x^2+10x-1 =0$.