The Fundamental Theorem of Algebra Is:
Every polynomial equation of
degree n, n>0, with complex coefficients has at least one complex root.
This is often stated as
Every polynomial equation of
degree n with complex coefficients has n roots in the complex numbers.
In fact, the two statements are equivalent. The second can be proved by
using the first form to know there is a root, and and then repeatedly dividing
the polynomial by one of its roots until its degree becomes zero.
Internet References
Wikipedia:
Fundamental theorem of algebra
Mathworld:
Fundamental Theorem of Algebra
Related pages in this website
Other so-called "fundamental" theorems
The Fundamental Theorem of
Arithmetic says every number has exactly one unique prime
factorization.
The Fundamental Theorem of
Calculus says if f is the derivative of F, then the integral from a to
b of f(x) dx is F(b)-F(a).
