P($s$) = $(s+\alpha+ e^{-s\tau})$
Proof that for $\alpha > 0$ and $\tau \geq 0$ the polynomial has no solution less than zero.
I am having difficulty proving that for $\alpha > 0$ and $\tau \geq 0$, the polynomial below doesn't lead to a real negative part (in case the solution was imaginary).
$s+\alpha+ e^{-s\tau} = 0$