Finding the Roots of a Cubic Equation - An Excursion into Mathematics History

Published on
07/20/2005

Activity Overview

In this Derive™ activity, students understand how the software solves cubic equations and relate it to contributions made by del Ferro, Tartaglia, and Cardan in finding the method of solving cubic equations.

Before the Activity

See the attached DFW file for detailed instructions for this activity

Print pages from the attached DFW file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity Procedures:

Set up a 2D plot window

Enter the standard cubic equation and choose random values for its coefficients

Continue simplifying until values obtained for the variable, coeff, contains all non zero values

Define a function and expand it so that the function is seen as a cubic

Adjust the scale and plot a graph that includes both the maximum and minimum values of the function

Shift the axes, and eliminate the squared term in the cubic equation by making a substitution for x in terms of another variable

Expand the result in terms of the new variable

Find the value which causes the coefficient of the squared term to be zero

Substitute the value in the expression and observe that the resulting cubic in the new variable has no squared term

Substitute the new variable with yet another quantity

Simplify the expression, work backwards, and determine the value of x

By factoring, find all the values of x that satisfy the standard cubic expression

After the Activity

Students answer questions listed on the activity sheet.

Review student results:

As a class, discuss questions that appeared to be more challenging