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 October 15th, 2011, 09:31 AM #1 Newbie   Joined: Jul 2010 Posts: 15 Thanks: 0 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?
 October 15th, 2011, 10:49 AM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: polynomial roots This might help... http://en.wikipedia.org/wiki/Descartes%27_rule_of_signs
 October 15th, 2011, 11:42 AM #3 Newbie   Joined: Jul 2010 Posts: 15 Thanks: 0 Re: polynomial roots Tanks, but Descarte rule doesn,t work for complex roots.
 October 15th, 2011, 09:51 PM #4 Member   Joined: Aug 2010 Posts: 32 Thanks: 0 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 $z^2=-1$ is a polynomial on complex field with two roots, namely $\pm i$. You can not say which is negative and which is positive, as these terms has no meaning in this context.
 October 17th, 2011, 03:51 AM #5 Newbie   Joined: Jul 2010 Posts: 15 Thanks: 0 Re: polynomial roots Actually I want the necessary condition guarantee that all roots hold in left half of the complex plan.
October 17th, 2011, 11:41 AM   #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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