Complex Roots of a Polynomial and Its Derivative

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

For a polynomial , the roots of (red) always lie within the convex hull of the roots of (cyan). Drag the locators, which are the roots of scaled up.


The red curve is the image of the unit circle transformed by the derivative of the polynomial. Use the checkbox "range mesh" to see the image of the grid ("domain mesh"), again under the map .


Contributed by: Michael Schreiber (March 2011)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.