All Questions

This is a lemma I wanted in order to solve Patrizio Neff's conjecture. It turned out to be the wrong way to think about it, but I am still curious if it is true. Let $z^n+a_{n-1} z^{n-1} + \cdots + ...

Suppose we have a polynomial function $f(z)=a_0+a_1z+a_2z^2+...+z^n$ with each $a_i$ between 0 and 1. Is there a method to determine if $f$ has a pair of complex conjugate roots? There are many ...

Is it true that the smallest root $t$ of the polynomial $$ 20 t^3 - 30 t^2 + (12 - 4 \cos^2 \alpha - 4 \cos^2 \beta - 4 \cos^2 \gamma) t + \cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma - 2 \cos \alpha \...