ABSTRACT
Back to square one. In Chapter 2 we proved the Fundamental Theorem of Algebra, Theorem 2.4,
using some basic point-set topology and simple estimates. It is also possible to give an ‘almost’ algebraic proof, in which the only extraneous information required is that every polynomial of odd degree overR has a real zero. This follows immediately from the continuity of polynomials overR and the fact that an odd degree polynomial changes sign somewhere between −∞ and +∞.
