Consider a polynomial of the following type:(adsbygoogle = window.adsbygoogle || []).push({});

A_n w^n + A_{n-1} w^{n-1}k + A_{n-2} w^{n-2} k^2 + ... + A_1 k^n =0

What are the general conditions on {A_i} in order for the roots w(k) to be EITHER real OR functions with even imaginary parts, Im[w[k]]=Im[w[-k]]?

I would be interested in whether anyone has ever worked on this problem, or if this problem was ever shown to be unsolvable (perhaps there is a trivial connection to, e.g., Galois theory I missed).

Thanks, and best

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A general condition on polynomial roots

Loading...

Similar Threads for general condition polynomial | Date |
---|---|

A Reality conditions on representations of classical groups | Jan 29, 2018 |

A What separates Hilbert space from other spaces? | Jan 15, 2018 |

A Galois theorem in general algebraic extensions | Apr 29, 2017 |

I Generalizing the definition of a subgroup | Feb 20, 2017 |

**Physics Forums - The Fusion of Science and Community**