The Fundamental Theorem of Algebra: From The Four Basic Operations
  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. 
Oswaldo Rio Branco de Oliveira
math.CA math.HO