Sliding the Roots of Cubics

The roots of a cubic polynomial depend on the coefficients of the cubic in a complicated way. In this Demonstration, you move the roots in the complex plane by varying the coefficients of the cubic.
If the coefficients , , and of a cubic are real, the cubic will have either three real roots or one real root and a pair of roots that are complex conjugates of each other. For some combinations of coefficients, two roots will slide along the real axis, then merge (forming a double root), then split and move off the real axis to become a pair of complex conjugate roots.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Related Curriculum Standards

US Common Core State Standards, Mathematics