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.
Wikipedia: Fundamental theorem of algebra
Mathworld: Fundamental Theorem of Algebra
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).
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