# What Is the Quadratic Formula?

The roots of the equation (the values of x that make y = 0) are given by the quadratic formula:

Step 1
Find the values of a, b and c.
a = 2, b = -5, c = 2.

Step 2
Insert the values of a, b and c into the quadratic formula and simplify:

Step 3
Find the root x1 that results from turning the ± into a +.

Step 4
Find the root x2 that results from turning the ± into a -.

The solution to the quadratic equation is x = 2 or x = ½.

# A Real Example of How to Solve Quadratic Equations Using the Quadratic Formula

Sometimes quadratic equations have repeated roots - that is the same number solves the quadratic equation twice.

The slider below shows how to solve a quadratic equation where there are repeated roots.
##### Interactive Test
show

2 ROOTS!

Quadratic equations have 2 roots, and the quadratic equation finds both of them.

Look closely at the formula, and you'll see a ± sign:

This means it is + one time, and - the other. This gives 2 roots:

# THE DISCRIMINANT

The term in the formula that appears in a square root is called the discriminant:

It discriminates between the 3 possible cases for the roots of a quadratic equation.

• b2 - 4ac > 0 - there are 2 real, distinct roots.

• b2 - 4ac = 0 - there is one repeated root.

• b2 - 4ac < 0 - there are 2 complex roots.

• # BE CAREFUL WITH SIGNS

a, b and c may be negative. Make sure you remember this when inserting them into the equation - write them inside brackets if need be.