Article View: sci.math.num-analysis
Article #1184Re: All Roots to any Polynomial
From: Alex.Lupas
Date: Wed, 04 Aug 2004 07:55
Date: Wed, 04 Aug 2004 07:55
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1886 bytes
Jon <jon8338@peoplepc.com> wrote in message news:<410E45F8.3090004@peoplepc.com>...
> In this development all roots to any degree polynomial are found to any
> desired degree of precision.
> http://www.geocities.com/jongiff2000/a7_polynomial_roots_bingo.html
> Jon Giffen
Consider the polynomial
P(x):=10*{-40}*x^6 - 3*10^{40}x^5-375*10^{38}*x^4+Ax^3+Bx^2+Cx+D .
It is known that :
a) P has only real roots x_j, 1 =< j=< 6 , and
b) if it is assumed that
x_1 =< x_2 =< x_3 =< x_4 =< x_5 =< x_6 ,
then x_5= 0.5 - sqrt(5).
Please help : find (with your method) x_1,x_2,x_3,x_4 and x_6 .
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X-Google-Thread: 107079,7d694ccd9df54fc5 X-Google-Thread: 109d8a,7d694ccd9df54fc5 X-Google-Thread: f72df,7d694ccd9df54fc5 X-Google-Thread: 103471,7d694ccd9df54fc5 X-Google-Thread: 1139f8,7d694ccd9df54fc5 X-Google-Thread: 10d67e,7d694ccd9df54fc5 X-Google-Thread: 1130d6,7d694ccd9df54fc5 X-Google-Thread: f6df2,7d694ccd9df54fc5 X-Google-Attributes: gid107079,gid109d8a,gidf72df,gid103471,gid1139f8,gid10d67e,gid1130d6,gidf6df2,public X-Google-Language: ENGLISH,ASCII-7-bit Path: arc1-ca.pugleaf.net!g2news1.google.com!postnews2.google.com!not-for-mail From: alexandru.lupas@ulbsibiu.ro (Alex.Lupas) Newsgroups: sci.math.num-analysis,sci.math,japan.sci.math,han.sci.math,fr.sci.maths,aus.mathematics,alt.math.recreational,bln.sci.mathematik Subject: Re: All Roots to any Polynomial Date: 4 Aug 2004 00:55:34 -0700 Organization: http://groups.google.com Lines: 20 Message-ID: <117ac0e5.0408032355.630ee9fa@posting.google.com> References: <410E45F8.3090004@peoplepc.com> NNTP-Posting-Host: 193.226.29.98 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1091606134 25700 127.0.0.1 (4 Aug 2004 07:55:34 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Wed, 4 Aug 2004 07:55:34 +0000 (UTC)