jheimann@bbncc5.UUCP (John Heimann) (10/11/85)
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Scipione del Ferro and Niccolo Tartaglia seperately discovered a
general closed form solution to cubic equations, sometime in the early 16th C.
It was published by Geronimo Cardano in 1545, and hence is known as Cardan's
Formula. Jacobson (_Basic Algebra I_, W.H. Freeman & Co., 1974) states (and
later derives) the formula in chapter 4 ("Galois Theory of Equations"). I'd
copy it here but it's a bit involved and I'm sure you can find it in a CRC
handbook.
Cardano also published a solution for 4th degree equations. It can be
shown (if you struggle through Jacobson) that the general 5th degree equation
is unsolvable. Actually, it's worth the struggle. Galois theory is very
beautiful, and can be used to solve other famous problems, such as proving it's
not possible to trisect an angle or duplicate a cube, proving pi and e are
transcendental, etc.
John