The Product of the Squares of the differences of the Polynomial Roots
. For a Polynomial of degree ,

(1) |

The discriminant of the Quadratic Equation

(2) |

(3) |

(4) |

The discriminant of the Cubic Equation

(5) |

(6) |

(7) | |||

(8) |

However, using the general definition of the polynomial discriminant for the standard form Cubic Equation

(9) |

(10) |

(11) |

The discriminant of a Quartic Equation

(12) |

(13) |

**References**

Beeler, M.; Gosper, R. W.; and Schroeppel, R. *HAKMEM.* Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972.

© 1996-9

1999-05-24