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 Math Help > Basic Algebra > Polynomial > Fundamental Theorem of Algebra

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).

The webmaster and author of this Math Help site is Graeme McRae.