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From: gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>)
Newsgroups: net.math
Subject: Re: cubic roots
Message-ID: <2071@brl-tgr.ARPA>
Date: Fri, 11-Oct-85 19:18:38 EDT
Article-I.D.: brl-tgr.2071
Posted: Fri Oct 11 19:18:38 1985
Date-Received: Mon, 14-Oct-85 06:16:41 EDT
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>   O.K. I take it there just aren`t any easy-as-pie ways
>   to find the roots to a cubic eqaution except synthetic
>   division, which doesn`t seem to work always. How do you
>   know when not to use synth division, and of the many 
>   other baroque methods, which are most popular? What 
>   indicators do you look out for, etc.?

Synthetic division is useful for factoring out one of the
primitive polynomials, once you have found it, thereby
reducing the degree of the polynomial.

However, all polynomials through quartics have exact
analytical solutions, which can be found in math handbooks.
Computationally, care must be taken or one gets incorrect
results.  E.g., exponents can overflow if you don't scale.