The use of zeroes to obtain a factored form for a polynomial is well known, as is the expansion of the coefficients as symmetric functions of the roots. If

P(z) |
= | (92) | |

= | (93) |

then

a_{1} |
= | (94) | |

a_{2} |
= | (95) | |

a_{3} |
= | (96) | |

a_{n} |
= | (97) |

In particular, if any

Of course, the reverse process, determining the zeroes given the coefficients, is more difficult and is the subject of much numerical analysis.