# The solution of a quadratic equation

The solution of quadratic equation, including complex roots

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

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