How to Solve Quadratic Equations Using the Quadratic Formula (Mathematics Lesson)
What Is the Quadratic Formula?
The quadratic formula is a way of solving a quadratic equation.For a quadratic equation:
The roots of the equation (the values of x that make y = 0) are given by the quadratic formula:
How to Solve a Quadratic Equation Using the Quadratic Equation
Question: Solve the quadratic equation below using the quadratic formula:Step 1
a = 2, b = -5, c = 2.
Step 2
Step 3
Step 4
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
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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:
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:
Note
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.
- b^{2} - 4ac > 0 - there are 2 real, distinct roots.
- b^{2} - 4ac = 0 - there is one repeated root.
- b^{2} - 4ac < 0 - there are 2 complex roots.