Education Technology

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
  • Re-teach concepts as necessary