The fundamental theorem of algebra: A most elementary proof

TL;DR

This paper presents an elementary, direct proof of the Fundamental Theorem of Algebra that avoids complex analysis tools, using only basic theorems like Bolzano-Weierstrass and the Binomial Formula.

Contribution

It introduces a novel, simplified proof of the theorem that does not rely on advanced calculus or trigonometry, making it more accessible.

Findings

Provides an elementary proof of the Fundamental Theorem of Algebra

Avoids complex analysis and advanced mathematical tools

Simplifies understanding of the theorem's foundation

Abstract

This paper shows an elementary and direct proof of the Fundamental Theorem of Algebra, via Bolzano-Weierstrass Theorem on Minima and the Binomial Formula, that avoids: any root extraction other than the one used to define the modulus function over the complex plane, trigonometry, differentiation, integration, series, arguments by induction and arguments using epsilon's and delta's.