Invariably, all roots of a cubic equation can be found using complex numbers (following the method of Cardan).

There is one solution method for all roots (real and complex), all cases.
The formulas I found online avoid using complex arithmetic (which computers and calculators don't always recognize). I think these formulas make it harder to handle the general problem.
Here, there are always three complex solutions, and whenever the imaginary part is zero, then the root is real.
For an iterative (root-hunting) solution: http://www.geogebratube.org/material/show/id/143036
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So the cubic has a solution. But for polynomials of arbitrary order, algebraic solution is not possible. Let me return to the methods used in the previous worksheet, and see what generalizations I can make....