Analytical solutions of cubic and quartic equations


by Curious3141
Tags: analytical, cubic, equations, quartic, solutions
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Apr30-06, 11:41 AM
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Even though it is uncommon to see questions asking for an analytical solution to equations of degree 3 or 4, they have been asked on the forum. It's also good to know how, in any case.

Cubic : http://www.karlscalculus.org/cubic.html

Quartic : http://www.karlscalculus.org/quartic.html

For the cubic equation, I would discourage simply memorising the general formula; instead, try to understand the method and remember the form of the required substitutions to reduce the cubic to a quadratic.

IMHO, the cubic is still doable by hand. The quartic is often too tedious to contemplate solving analytically (without a computer), but the method is instructive.
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