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From: KAZLOWF%PACEVM.BITNET@CUNYVM.CUNY.EDU (Michael Kazlow)
Newsgroups: comp.sys.handhelds
Subject: RE: Finding roots of Tertiary and above equations?
Message-ID: <5A91CE3760006506@gacvx2.gac.edu>
Date: 10 Apr 91 06:03:47 GMT
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Return-path: <@CUNYVM.CUNY.EDU:KAZLOWF@PACEVM.BITNET>
In-reply-to: Your message of Tue, 9 Apr 1991 23:45 CST
To: handhelds@gac.edu

It is impossible to find a general solution to a polynomial equation that
has real or complex coefficients that can be expressed in terms of elementary
functions that use radicals square roots, cube roots, etc.:  The proof of
this result uses Galois Theory.  It can be found in most abstract algebra
written for first year graduate mathematics students.  It is also in many
undergraduate texts. Note: The lack of a general formula is true for
polynomials of degree of at least five:.

This does not mean there is no general formula that use non-elementary
functions.  However, noone knows of such a formula!

Galois Theory can be used to show two other classical problems have no
solution: Squaring the circle and trisecting an angle with compass and straight
edge.

For the mathematically inclined Galois Theory is beautiful mathematics.

 From the computer of: Michael Kazlow (Bitnet: KAZLOWF@PACEVM)
Acknowledge-To: <KAZLOWF@PACEVM>