The fundamental theorem of algebra is a proven fact about polynomials, sums of multiples of integer powers of one variable. It is based on mathematical analysis, the study of real numbers and limits. It was first proven by German mathematician Carl Friedrich Gauss. It says that for any polynomial \displaystyle{ f(x) } with the degree \displaystyle{ n }, where \displaystyle{ n\gt 0 }, the polynomial equation \displaystyle{ f(x)=0 } must have at least one root \displaystyle{ x }, and not more than \displaystyle{ n } roots altogether.