# The solution of a quadratic equation

The solution of quadratic equation, including complex roots

### This page exists due to the efforts of the following people:

#### Timur

Created: 2011-07-23 20:16:59, Last updated: 2021-03-12 16:49:46 This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/168/. Also, please do not modify any references to the original work (if any) contained in this content.

A quadratic equation is a second-order polynomial equation in a single variable x

with a != 0

The roots x can be found using the quadratic formula

There are three cases:

if
then there are two distinct roots, both of which are real numbers

if
then there is exactly one distinct real root, sometimes called a double root

if
then there are no real roots. Rather, there are two distinct (non-real) complex roots.

The expression

is called the discriminant of the quadratic equation

Using roots, polynomial equation can be expressed as

Below the calculator Digits after the decimal point: 2
x1

x2

URL copied to clipboard

#### Similar calculators

PLANETCALC, The solution of a quadratic equation