The Fundamental Theorem of Algebra: From The Four Basic Operations

TL;DR

This paper provides an elementary, direct proof of the Fundamental Theorem of Algebra using the Bolzano-Weierstrass Theorem, avoiding complex methods like root extraction, non-algebraic functions, and induction.

Contribution

It introduces a novel proof of the Fundamental Theorem of Algebra that is elementary and avoids traditional advanced techniques.

Findings

Proof relies solely on elementary analysis and the Bolzano-Weierstrass Theorem.

Avoids complex methods such as root extraction, angle arguments, and non-algebraic functions.

Simplifies understanding of the Fundamental Theorem of Algebra for foundational mathematics.

Abstract

This paper presents an elementary and direct proof of the Fundamental Theorem of Algebra, via Bolzano-Weierstrass Theorem on Minima, that avoids: every root extraction, angle, non-algebraic functions, differentiation, integration, series and arguments by induction.