Alternate Form of the Quartic Formula

Background

The material herein concerns finding the four solutions to

The Formula

The material on this page is actually the same as on the "Solving Polynomials" page, and is the same as in the Roots of Polynomials document, except that, instead of leaving the solution to a quartic in terms of a resolvent cubic (eqn. 14 in the "Roots of Polynomials" document), the resolvent cubic is solved explicitly (using the methods on the Alternate Form of the Cubic Folrmula page. This leaves an explicit, easier to evaluate, form of the Quartic Formula.

This explicit form is written out in The Quartic Formula document.

TI-84 Program

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

Examples

Here are a few examples which use this form of the Quartic Formula. When going through the examples, it is most advantageous to calculate all the cube and square roots with your graphing calculator, and also, to store all intermediate calculated results in your calculator. In this way maximum accuracy is achieved. Alternatively, these examples may serve as test cases for the above TI-84 program.