# Discriminant

### What is it and how do you find it?

## What is it?

The discriminant is a number calculated by using the formula b^2-4ac.

If its value is positive (greater than zero), the quadratic has 2 solutions.

If its value is zero, the quadratic has 1 solution.

If its value is negative (less than zero), the quadratic has 2 complex (imaginary) solutions.

## How do you find it?

## Try these...

Find the discriminant and describe the number and type of roots.

1. x^2-9=3x

2. 4x^2+10x+9=0

3. 9x^2+12x+4=0

1. x^2-9=3x

2. 4x^2+10x+9=0

3. 9x^2+12x+4=0

## Your answers...

## #1 First, put the equation in standard form. Then plug in you a, b and c. Your discriminant is 45 which means you have 2 real solutions. | ## #2 Plug your a, b and c into the formula. Your discriminant is -44 which means you have 2 complex (aka imaginary) solutions. | ## #3 Plug in a, b, and c. Your discriminant is zero which means you have 1 real solution. |

## #1

First, put the equation in standard form. Then plug in you a, b and c. Your discriminant is 45 which means you have 2 real solutions.

## #2

Plug your a, b and c into the formula. Your discriminant is -44 which means you have 2 complex (aka imaginary) solutions.

## What does this mean?

If you graphed #1, it would intersect the x-axis 2 times.

If you graphed #2, it would not intersect the x-axis at all.

If you graphed #3, it would sit on the x-axis, intersecting it one time.

If you graphed #2, it would not intersect the x-axis at all.

If you graphed #3, it would sit on the x-axis, intersecting it one time.