The Quadratic equation reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Quadratic equation

A quadratic equation is a polynomial equation of degree 2. The generalized form is ax² + bx + c = 0. For example,

5x² + 3x + 4 = 0.

The numbers 5, 3 and 4 here are called coefficients: 5 is the coefficient of x² and 3 is the coefficient of x.

A quadratic equation with real or complex coefficients has two complex roots (i.e., solutions), although the two roots may be equal. These roots can be computed using the quadratic formula.

Higher order equations may be quadratic in form, such as:

2x⁶ + 3x³ + 5 = 0.

Note that the highest exponent is twice the value of the exponent of the middle term. This equation may be resolved directly or with a simple substitution, using the methods that are available for the quadratic, such as factoring, the quadratic formula, or completing the square.

See also: linear equation, cubic equation, quartic equation, quintic equation, fundamental theorem of algebra

This is the "Quadratic equation" reference article from the English Wikipedia. All text is available under the terms of the GNU Free Documentation License. See also our Disclaimer.