Carl Friedrich Gauss

Abstract

The most important contributions of Gauss to the theory of algebraic equations are: first, the complete solution of the “cyclotomic equation”

$$ {x^m} - 1 = 0 $$

((1))

by means of radicals, second, the proof that every polynomial in one variable with real coefficients is a product of linear and quadratic factors. This theorem implies what we now call the “fundamental theorem of algebra”: Every polynomial f(x) with complex coefficients is a product of linear factors.