Zeros of polynomial vs derivative @drpeyam

Uploaded February 2022 | Updated September 2026, 1 week ago

We will see how the zeros of the derivative of a polynomial are related to the zeros of the original polynomial. This is called the Gauss Lucas Theorem for zeros of derivatives, which is an elegant result from complex analysis that relates it with the convex hull of the original roots. I also mention Marden's theorem, which is a special case of a triangle, and which has to do with the Steiner inellipse and foci. Enjoy this geometry and calculus adventure.

0:00 Introduction
0:09 Roots of P
3:00 Plotting the roots geometrically
5:15 Gauss Lucas Theorem
6:52 Marden's Theorem

Gauss Lucas (full version): youtu.be/5DwKA9MVt-Q (members only)
Gauss Lucas Proof: youtu.be/phthkaWOx6o (members only)
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