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High order polynomials

  1. Nov 3, 2015 #1
    Hello

    I am working on high order polynomials and I have two questions:


    1. Is there a method other than the one based on the "synthetic division with testing the signs" for identifying the lower and upper limits of the real roots?

    2. Is there a way for identifying the smallest interval on the x-axis between two successive real roots, i.e. is there a theorem or test that can provide a limit on the size of the x-interval that separates successive real roots without knowing the roots?

    Thank you for your help!
     
  2. jcsd
  3. Nov 3, 2015 #2

    Krylov

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  4. Nov 3, 2015 #3

    mathman

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    https://en.wikipedia.org/wiki/Sturm's_theorem

    The above describes a method to obtain intervals to bracket individual real roots. I believe it can be adapted to answer your questions.
     
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