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From: seroussi@hplred.HP.COM (Gadiel Seroussi)
Newsgroups: comp.sys.handhelds
Subject: Re: Finding roots of Tertiary and above equations?
Message-ID: <6230005@hplred.HP.COM>
Date: 10 Apr 91 16:48:00 GMT
References: <25744@hydra.gatech.EDU>
Organization: Hewlett Packard Labs, Palo Alto CA
Lines: 19

In / hplred:comp.sys.handhelds / hoford@sequoia.circ.upenn.edu (John Hoford) /  7:25 am  Apr  9, 1991 /
John Hoford says:

> I gusss what I am asking is, what does it meen to say something
> has an algebraic soloution and
> is ther any thing realy special about 5'th and above degree
> polynomials.

A number is "algebraic" if it is the root of a polynomial with rational 
coefficients. A number is "trascendental" if it is not. Thus, all polynomials
with rational coefficients have "algebraic" roots, regardless of their degree.
However, for polynomials f(x) of degree n >= 5, there is no 
"solution by radicals".  This means you cannot write finite formulas, 
involving arithmetic operations and m-th roots of any order, that will give 
you the solutions of f(x)=0 as symbolic functions of the coefficients of
f. Of course, such formulas are known for n=1,2,3,4.

Gadiel Seroussi
HP Labs