Strictly Real Fundamental Theorem of Algebra
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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Classical Analysis and ODEs
26C10, 65H04, 26B35
