# Fundamental theorem of algebra

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 altogether. A root is a number x so that $f(x) = 0$.
• 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