User:Blankuser/Cohn Schur Criterion

The quadratic equation formed from $$\rho(w)-z\sigma(w)$$ and rearranged:

$$aw^2+bw+c,a,b,c\in\mathbb{C}$$

obeys the root condition if and only if:

$$\left|a\right|^2-\left|c\right|^2\ge 0$$

$$\left(\left|a\right|^2-\left|c\right|^2\right)^2\ge\left|a\bar{b}-b\bar{c}\right|^2$$

and if the latter is obeyed as an equality then:

$$\left|b\right|<2\left|a\right|$$.