Every Polynomial equation having Complex Coefficients and degree has at least one Complex Root. This theorem was first proven by Gauß. It is equivalent to the statement that a Polynomial of degree has values of (some of them possibly degenerate) for which . An example of a Polynomial with a single Root of multiplicity is , which has as a Root of multiplicity 2.

**References**

Courant, R. and Robbins, H. ``The Fundamental Theorem of Algebra.'' §2.5.4 in
*What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed.*
Oxford, England: Oxford University Press, pp. 101-103, 1996.

© 1996-9

1999-05-26