Alternate Form of the Cubic Formula

Background

I teach this material in my senior Plane Trigonometry class at East High, after the students have learned how to calculate the three cube roots of a real (or complex) number, i.e., after they have learned to apply De Moivre's Theorem. In any case, the material herein concerns finding the three solutions to

The Formula

The derivation of the formula is probably beyond most high school students, but it is included here, if you are interested. The actual formula is located in this document, which I distribute to the students.

TI-84 Program

Here is a listing of a TI-84 program which implements this form of the Cubic Formula.

Examples

Here is a set of example problems. When going through them (with yourself or with your students) it is most advantageous to store all intermediate results in your calculator (it's easier, and most accurate). Alternatively, these may serve as test cases for the above TI-84 program.