*World of Mathematics*. ©2005-2006 Thomson Gale, a part of the Thomson Corporation. All rights reserved.

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## Quadratic Equations

A quadratic equation is a second order, univariate polynomial with constant coefficients and can usually be written in the form: *ax*^{2} + *bx* + *c* = 0, where *a* 0. In about 400 B.C. the Babylonians developed an algorithmic approach to solving problems that give rise to a quadratic equation. This method is based on the method of **completing the square**. Quadratic **equations**, or **polynomials** of second-degree, have two **roots** that are given by the quadratic formula: *x* = (-*b* +/- (*b*^{2} - 4*ac*))/2*a*. There is another form of this equation yielding the roots for a quadratic equation that is obtained by first dividing the original quadratic equation through by *x*: *x* = (2*c*)/(-*b* +/- (*b*^{2} - 4*ac*)). This equation, which provides the roots to the quadratic equation, is often useful when *b*^{2} > 4*ac*. In these cases the usual form providing roots to the quadratic equation can yield...

This section contains 607 words(approx. 3 pages at 300 words per page) |