Roots of sum of factorized polynomials?

Christer · 2nd July 2007, 04:41 PM

Consider the sum of two factorized polynomials:

k1(s+a1)...(s+am) + k2(s+b1)...(s+bn)

is there some nice theorem telling us something about the roots of this sum? A theorem that tells us all the roots algebraically would be grand slam.

Cal Weldon · 2nd July 2007, 07:36 PM

The bear is white. I'm afraid I'm no help with the other question.

Christer · 2nd July 2007, 07:54 PM

Oh, well. Poles are involved in both questions, at least.

BWRX · 2nd July 2007, 08:33 PM

Quote:

Originally posted by Christer
is there some nice theorem telling us something about the roots of this sum?

Yes, it is called MATLAB

Alternatively, there is a cool freeware program called Maxima that might be able to help out.
http://wxmaxima.sourceforge.net/wiki....php/Main_Page

Christer · 2nd July 2007, 10:02 PM

Quote:

Originally posted by BWRX

Yes, it is called MATLAB

Alternatively, there is a cool freeware program called Maxima that might be able to help out.
http://wxmaxima.sourceforge.net/wiki....php/Main_Page

I actually used to have Maxima installed, but haven't yet reinstalled since my last sytem reinstall. I admit I didn't think of that possibility, but I must say I question whether either Maxima or Matlab could present a general algebraic solution unless there already are some useful theorems they can apply. Oh well, maybe I should get Maxima up and running and see if can do it.

jacco vermeulen · 2nd July 2007, 10:04 PM

Quote:

Originally posted by Christer
unless there already are some useful theorems they can apply.

Eeh, you don't know ?

Blues · 2nd July 2007, 10:12 PM

Quote:

Originally posted by Cal Weldon
The bear is white. I'm afraid I'm no help with the other question.

I'm afraid the white bear should have found itself 10km to the west of where it started unless it walks another 10km to the east...

Christer · 2nd July 2007, 10:16 PM

Quote:

Originally posted by jacco vermeulen

Eeh, you don't know ?

What do you mean I don't know?

I don't know of any theorems of the kind I was asking for, but hope there might be something of the kind, despite me not knowing it.

Christer · 2nd July 2007, 10:51 PM

I have tried Maxima now, and it seems not possible to do what I was asking, or at least I can't see any way of doing it. It seems not to like constant symbols, but want numerical values for them, in order to even accept the polynomial for finding roots. And for the general problem that I stated, I am not sure there is even a way to enter the problem unless we fix m and n.

darkfenriz · 3rd July 2007, 12:06 AM

I am affraid, that if order is higher than 5 algebraic solutions may not exist. Numerical solutions are possible.

2nd July 2007, 04:41 PM	#1
Christer diyAudio Member Join Date: Sep 2002 Location: Sweden	Roots of sum of factorized polynomials? Consider the sum of two factorized polynomials: k1(s+a1)...(s+am) + k2(s+b1)...(s+bn) is there some nice theorem telling us something about the roots of this sum? A theorem that tells us all the roots algebraically would be grand slam.

2nd July 2007, 07:36 PM	#2
Cal Weldon Speakerholic diyAudio Moderator Join Date: Jan 2004 Location: British Columbia	The bear is white. I'm afraid I'm no help with the other question. __________________ Next stop: Margaritaville Some of Cal's stuff \| Cal Weldon Consulting

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2nd July 2007, 07:54 PM	#3
Christer diyAudio Member Join Date: Sep 2002 Location: Sweden	Oh, well. Poles are involved in both questions, at least.

2nd July 2007, 10:51 PM	#9
Christer diyAudio Member Join Date: Sep 2002 Location: Sweden	I have tried Maxima now, and it seems not possible to do what I was asking, or at least I can't see any way of doing it. It seems not to like constant symbols, but want numerical values for them, in order to even accept the polynomial for finding roots. And for the general problem that I stated, I am not sure there is even a way to enter the problem unless we fix m and n.

3rd July 2007, 12:06 AM	#10
darkfenriz diyAudio Member Join Date: Jun 2004 Location: Warsaw	I am affraid, that if order is higher than 5 algebraic solutions may not exist. Numerical solutions are possible.

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