# Discriminants

The discriminant of a quadratic equation will tell you how many roots the quadratic equation has.

Solutions of a quadratic equation are known as roots; they can be seen on the graph of a quadratic where the graph crosses the x-axis. Recall that the general quadratic equation: , can have two distinct roots, one repeated roots or no roots at all (unless you are working with complex numbers).

The discriminant can tell you how many roots a quadratic equation will have without having to actually find them.

For the quadratic equation , the discriminant is given by .

**If , the equation has two distinct roots.****If , the equation has one repeated root.****If , the equation has no roots.**

## Example 2

A quadratic has equation .

- Calculate the discriminant of the quadratic.
- Given that the quadratic has two distinct roots, find the possible values of p.