On Mon, Sep 22, 2008 at 6:36 PM, W F <amzoti at gmail.com> wrote:
> ...Here is the real solution - but there are two imaginary ones too.
>
Not quite. This is a general cubic equation. Assuming that a,b,c,d are
real, then it may have either one real and two complex roots, two real roots
(one of multiplicity 2), or three real roots. If there are three real
roots, they cannot in general be expressed by a formula in radicals all of
whose subparts are real; see
http://en.wikipedia.org/wiki/Casus_irreducibilis. So there may be real
solutions "hiding behind" the complex expressions.
The symbolic solution of cubic polynomials is not very often useful except
of course if there is some interesting relationship among the coefficients.
-s