October 15th, 2011, 10:31 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, 11:49 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, 12:42 PM  #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, 10:51 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 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. 
October 17th, 2011, 04:51 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, 12:41 PM  #6  
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: polynomial roots Quote:
 

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