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Old 11-12-2009, 03:28 AM
Luna Moon
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Default range of roots of a polynomial?

x^6- p1*x^5-p2*x^4-p3*x^3-p4*x^2-p5*x - p6 = 0,

where p1+...+p6=1,

we know one root must be 1; other than that, under what conditions
will we be able to have the remain roots to be inside the unit circle?

Thanks
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Old 11-12-2009, 04:37 AM
Tim Wescott
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Default Re: range of roots of a polynomial?

On Wed, 11 Nov 2009 19:28:19 -0800, Luna Moon wrote:

> x^6- p1*x^5-p2*x^4-p3*x^3-p4*x^2-p5*x - p6 = 0,
>
> where p1+...+p6=1,
>
> we know one root must be 1; other than that, under what conditions will
> we be able to have the remain roots to be inside the unit circle?


Search for "Schur stability test" -- perhaps that'll help.

--
www.wescottdesign.com
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Old 11-12-2009, 09:33 AM
HardySpicer
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Default Re: range of roots of a polynomial?

On Nov 12, 5:37*pm, Tim Wescott <[email protected]> wrote:
> On Wed, 11 Nov 2009 19:28:19 -0800, Luna Moon wrote:
> > x^6- p1*x^5-p2*x^4-p3*x^3-p4*x^2-p5*x - p6 = 0,

>
> > where p1+...+p6=1,

>
> > we know one root must be 1; other than that, under what conditions will
> > we be able to have the remain roots to be inside the unit circle?

>
> Search for "Schur stability test" -- perhaps that'll help.
>
> --www.wescottdesign.com


Or a Jury test.
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