and synthetic division.
Descartes Rule of Sign to determine possibilities
What technique is used to find zeros (real and complex) for something like:
f(x) = x³ - 3x² + 12
I know from discriminant that is has two complex roots, and I can estimate real root from graph, but don't know, algebraically, how to find exact answers.
Thanks for any help.
There is a "cubic equation", its a bit nasty but for this particular function could be worth a look.
The "Cubic Formula"
Messy but divide out the real linear factor leaving you with a quadratic, then use the quadratic formula to get the complex roots.
I would not do this by hand myself as that is too error prone, but would use a symbolic mathematics system (Maxima, of Wolfram Alpha are two obvious candidates)
CB
Well at least your not in denial, I respect this!
Have a read of this, it gives you a step by step to how to solve a cubic.
The "Cubic Formula"