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October 15th, 2011, 10:31 AM   #1
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polynomial roots

Hi,
Consider a polynomial of degree n:
A(s)=a1+a2*s+...+ai*s^n
What is the necessary conditions (in term of a1...ai) guarantee all roots of A(s) will be negative?
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October 15th, 2011, 11:49 AM   #2
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Re: polynomial roots

This might help...
http://en.wikipedia.org/wiki/Descartes%27_rule_of_signs
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October 15th, 2011, 12:42 PM   #3
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Re: polynomial roots

Tanks, but Descarte rule doesn,t work for complex roots.
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October 15th, 2011, 10:51 PM   #4
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Re: polynomial roots

Well, dealing with polynomials on complex field, the notion of "positive and negative root" has no meaning as we don't have any order on this field.
For example is a polynomial on complex field with two roots, namely . You can not say which is negative and which is positive, as these terms has no meaning in this context.
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October 17th, 2011, 04:51 AM   #5
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Re: polynomial roots

Actually I want the necessary condition guarantee that all roots hold in left half of the complex plan.
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October 17th, 2011, 12:41 PM   #6
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Re: polynomial roots

Quote:
Originally Posted by parastvand
Actually I want the necessary condition guarantee that all roots hold in left half of the complex plan.
That would actually be good to know upfront!
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