# 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 , $\u2102$ is algebraically closed^{}.

As a corollary, a non-constant polynomial in $\u2102[Z]$ 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 |