## Algebra## Polynomial Equations |

## What is a quadratic equation? |

A quadratic equation is a second degree (order) polynomial equation, thus it is guaranteed to have two solutions, both of which may be real or complex. This is seen in the standard form *ax*^{2} + *bx* + *c* = 0.

The roots of *x* can be found in the equation by factoring and completing the square (a method of transforming a quadratic equation so that it is in the form of a perfect square). For example, to solve the equation *x*^{2} - 3*x* = 4 by factoring, you would do the following:

First, write the equation in standard quadratic equation form:

Then factor the form:

In order for these numbers to equal zero, we determine that for (*x* - 4), *x* would be 4; and for (*x* + 1), *x* would equal -1. Thus, the solutions are 4 and -1.