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From: gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>)
Newsgroups: net.math,net.wanted
Subject: real roots of polynomial
Message-ID: <7942@brl-tgr.ARPA>
Date: Fri, 1-Feb-85 13:15:48 EST
Article-I.D.: brl-tgr.7942
Posted: Fri Feb  1 13:15:48 1985
Date-Received: Wed, 6-Feb-85 03:31:42 EST
Distribution: net
Organization: Ballistic Research Lab
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Xref: watmath net.math:1780 net.wanted:5707

I would appreciate constructive suggestions concerning fast, stable
methods for determining the real zeroes of a polynomial with real
coefficients.  I know of stable but slow methods and of fast methods
that occasionally run amok.  The polynomial in question is of degree
four, if that helps; more general solutions might be useful also.

For purposes of discussion, denote the polynomial:

	P(x) == a[0] + a[1]*x + a[2]*x^2 + a[3]*x^3 + a[4]*x^4

where a[i] are all real.  What is wanted is one or more real values
of x such that P(x) = 0.