Edit made on February 15, 2009 by GarethMcCaughan at 00:30:21
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An equation of the form EQN:ax^5+bx^4+cx^3+dx^2+ex+f=0
It is well know that the quadratic equation has a closed form solution.
It is well known that the quadratic equation has a closed form solution.
It is less well known that the cubic equation and quartic equation also
both have closed form solutions, although they are significantly more
For centuries a general solution for the quintic (and higher) equation
was sought, but in 1824 Abel proved that such a formula (using radicals)
is impossible, and this was generalised and extended by Galois's work of
1832 or so.