  This paper presents an alternative proof of the Fundamental Theorem of
Algebra that has several distinct advantages. The proof is based on simple
ideas involving continuity and differentiation. Visual software demonstrations
can be used to convey the gist of the proof. A rigorous version of the proof
can be developed using only single-variable calculus and basic properties of
complex numbers, but the technical details are somewhat involved. In order to
facilitate the reader's intuitive grasp of the proof, we first present the main
points of the argument, which can be illustrated by computer experiments. Next
we fill in some of the details, using single-variable calculus. Finally, we
give a numerical procedure for finding all roots of an n'th degree polynomial
by solving 2n differential equations in parallel.
