All Questions
2 questions
3
votes
2
answers
302
views
Finding the critical points of a degree $5$ Blaschke product
The derivative of a degree $5$ polynomial $p\in\mathbb{C}[z]$ is a degree four polynomial $p'\in\mathbb{C}[z]$, and as such, the zeros of $p'$ may be found explicitly using the quartic formulae.
One ...
10
votes
2
answers
728
views
Gauss--Lucas type theorem for tracts and higher derivatives of a polynomial
The Gauss--Lucas Theorem states that all zeros of derivative of a degree $n$ complex polynomial $p(z)$ are contained in the convex hull of the zeros of $p$. By iteration, this implies that the zeros ...