Strictly Real Fundamental Theorem of Algebra

2017/04/26 by Soham Basu, Basu, Soham
Computer Science · Mathematics · #26B35 #26C10 #65H04 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Polynomial and algebraic computation #math.CA #msc:26B35 #msc:26C10 #msc:65H04

paper · pdf · doi:10.48550/arxiv.1704.08312

openalex publication_date 2017/04/26 · arxiv created 2020/09/25 · arxiv updated 2020/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given any polynomial with real coefficients, the existence of a real quadratic polynomial factor is proven using only basic real analysis. The aim is to provide an approachable proof to anybody who is familiar with the least upper bound property for real numbers, continuity and growth property of polynomials, and unfamiliar with complex numbers, field extension or advanced topology.

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