It is given that A,B,C and D are roots of the quartic equation X^4 - X +2 = 0. Determine, whether or not (AB+CD) is a root of the equation X^3 – 8X –1 = 0.
(In reply to
Nothing elegant yet by goFish)
You are right, goFish: The three different
values for AB+CD you get by permuting the roots of X^4-X+2 give the
three different roots of X^3-8X-1. I had only considered one of
the roots. Hence we can solve a particular cubic if we can solve
a particular quartic. Is this a general thing? Smells like
Galois Theory (which is way beyond what we do on this site).
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Posted by Richard
on 2005-12-23 00:15:23 |
re: Nothing elegant yet
