The Fundamental Theorem of Algebra

Abstract

We saw in 3.3.5 that every quadratic polynomial vanishes at two (possibly coincident) points in ℂ, the zeros of the polynomial, as they are often called. This statement is a special case of a far more general theorem, which Gauss in 1849 (Werke 3, 73) called the fundamental theorem of the theory of algebraic equations, and which is now generally known in the literature as the so-called fundamental theorem of algebra.

Was beweisbar ist, soll in der Wissenschaft nicht ohne Beweis geglaubt werden (Dedekind 1887).

[In science, what is provable should never be believed without proof.]