Theory of algebraic equations

Abstract

Up to the middle of the 19th century, algebra was almost identical with the question of solving algebraic equations, particularly the nth degree equation in one indeterminate with real or complex coefficients. Hence the name “Fundamental theorem of algebra” for the theorem that each such equation has a complex number as solution. To solve an equation meant to present the solutions in terms of radicals. We make this concept precise in Sect. 7.1.