How do the roots of a polynomial relate to the roots of its derivative? - Complex Analysis
Channel: Jim Fowler
Date: 2021-03-29

This video presents a geometric proof of the Gauss-Lucas theorem, the fact that the roots of the derivative of a nonconstant polynomial sit within the convex hull of the roots of the polynomial.

I learned this argument from

  Arnaud Chéritat, Yan Gao, Yafei Ou, Lei Tan. A refinement of the Gauss-Lucas theorem (after W. P. Thurston) . 2015. ffhal-01157602f

which you can read at https://hal.archives-ouvertes.fr/hal-01157602/document

#complex #analysis #polynomial #phaseplot