Re: All Roots to any Polynomial

From: Alex.Lupas (alexandru.lupas_at_ulbsibiu.ro)
Date: 08/04/04 

Date: 4 Aug 2004 00:55:34 -0700

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 .