Skip to main content

All Questions

Filter by
Sorted by
Tagged with
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 ...
Trevor J Richards's user avatar
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 ...
Trevor J Richards's user avatar