Complete, algebraic solution for finding all roots of a cubic equation using complex algebra (following the method of Cardan).
I avoided formulas using the arccosine function. I think they needlessly complicate both hand and computer calculation. They also make it harder to ask the question, [i]Is there a unified, algebraic solution, or not?[/i].
(Yes, there is).
Notes:
Using this method, there are always three roots, each in the form (a + b[i]i[/i]). Whenever b =0, the root is real.
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Iterative solution: [url]http://www.geogebratube.org/material/show/id/143036[/url]
