Fundamental theorem of algebra

From Wikipedia, the free encyclopedia

The fundamental theorem of algebra is a proven fact that is the basis of mathematical analysis, the study of limits. It was proven by German mathematician Carl Friedrich Gauss. It says that for any polynomial f(x) with the degree n, where n>0, f must have at least one root, and not more than n roots alltogether. A root is a number x so that f(x) = 0.

Some remarks:

• the degree n of a polynomial is the highest power of x that occurs in it
• some of the roots may be complex numbers
• it is possible to 'count' the root r twice, if r is still a root of the polynomial g(x) = f(x) / (x − r); if you will 'count' the roots in this way, then the polynomial f(x) with degree n has exactly n roots
• many people say that the theorem's name is wrong because it is used more in analysis than algebra