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Solution of quadratic equation, including complex roots 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  PLANETCALC, Solution of quadratic equation