Routh-Hurwitz Theorem

Thread Starter

Zaryab Saeed

Joined Feb 10, 2016
3
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!

Papabravo

Joined Feb 24, 2006
16,472
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.

MrAl

Joined Jun 17, 2014
8,359
Hi,

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

Also:

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.
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.

Papabravo

Joined Feb 24, 2006
16,472
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.
Yes they can, but the answer was a response to the context of the original question.

MrAl

Joined Jun 17, 2014
8,359
Yes they can, but the answer was a response to the context of the original question.
Hi,

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

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