"Solving Polynomials with Computers," by Victor Y. Pan. American Scientist, January-February 1998, pages 62-69.
In mathematics, science, and engineering, the problem of solving a polynomial equation often arises. To solve a polynomial equation is to find values of the polynomial's variables that make the equation balance; this is also known as finding the roots of the polynomial. While there are formulas, like the quadratic formula, that produce the roots of certain simple polynomials, it was shown in the 19th century that there is no universal rule for finding the roots of all polynomials. However, mathematicians have developed many ingenious techniques for producing good approximate solutions. This article describes some of the history of this problem and discusses some speedy computer algorithms that have recently been developed.
--- Allyn Jackson