fundamental theorem of algebra

Theorem.

Let $f\mathrm{\in }\mathrm{C}\mathit{}\mathrm{[}Z\mathrm{]}$ be a non-constant polynomial. Then there is a $z\mathrm{\in }\mathrm{C}$ with $f\mathit{}\mathrm{(}z\mathrm{)}\mathrm{=}\mathrm{0}$.

In other , $ℂ$ is algebraically closed.

As a corollary, a non-constant polynomial in $ℂ[Z]$ factors completely into linear factors.

Title	fundamental theorem of algebra
Canonical name	FundamentalTheoremOfAlgebra
Date of creation	2013-03-22 12:18:56
Last modified on	2013-03-22 12:18:56
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	14
Author	Mathprof (13753)
Entry type	Theorem
Classification	msc 12D99
Classification	msc 30A99
Related topic	ComplexNumber
Related topic	Complex
Related topic	TopicEntryOnComplexAnalysis
Related topic	ZeroesOfDerivativeOfComplexPolynomial