Routh-Hurwitz Theorem

Discussion in 'Homework Help' started by Zaryab Saeed, Mar 20, 2016.

  1. Zaryab Saeed

    Thread Starter New Member

    Feb 10, 2016
    3
    0
    Hi, I have a problem in which, given a polynomial, I have to calculate the number of roots with positive, zero and/or negative real parts. Now I know that every sign change in the first column of the Routh array indicates the number of roots with a positive real part, but how do I find out the roots with negative and/or zero real parts? I've tried reading up on it, but couldn't find the answer to this anywhere. Any help would be appreciated. Thanks!
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,144
    1,790
    1. You can graph the polynomial.
    2. You can use synthetic division to search for x-axis intersections, then use Newton's method to refine the result.
    3. Roots with a zero real part are actually conjugate pairs.
    4. Use the quadratic formula after finding one or more real roots.
    5. Ask Matlab, Scilab, or Octave to give you the roots.
     
  3. MrAl

    Well-Known Member

    Jun 17, 2014
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    Hi,

    Do you have to use R.H. or can you use any method you choose?

    Also:

    I think a better wording for #3 is: "Roots with an imaginary part appear as conjugate pairs".
    They can have a non zero or zero real part.
     
  4. Papabravo

    Expert

    Feb 24, 2006
    10,144
    1,790
    Yes they can, but the answer was a response to the context of the original question.
     
  5. MrAl

    Well-Known Member

    Jun 17, 2014
    2,433
    490
    Hi,

    Yes, very good. I was being a bit more general with my reply.
     
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