This an update to the lesson I posted in an MHF thread a few months back.
This calculator solves 3 types of cubics:
Cubics with a discriminant = 0 which have 3 real roots, all equal.
Cubics with a discriminant < 0 which have 3 real unique roots.
Cubics with a discriminant > 0 which have 1 real root and 2 imaginary roots.
Just like the original thread, you can solve "the long way" using the method on Wikipedia or you can do a guess and check which works for real roots, then calls the synthetic division lesson, which then calls the quadratic lesson, all with push button link clicking. If you do the guess and check, each lesson click will take you to the next lesson for the next part of the journey.
I built method 2 for a user here on MHF, but the general consensus is that Method 1 is the way to go. Be advised the long way is quite a bit of math to go through and digest.
The lesson is located on the algebra page, searchable by cubic, equation, roots, synthetic.
Let me know if you want enhancements or see fixes.
Solving Cubic Equations