In the link bellow
Showing an equation has one positive root,
It has been shown that the considered equation has exactly one positive root. What can we do in order to compute an upper and a lower bound for $Cond(p)(\beta)$ where $Cond(p)(\beta)$ is the condition number for this root?
My attempt:
I tried to use the formula bellow
$Cond(p)(a)=\frac{\vert a \rvert \lvert p(a)^{'}\rvert}{\lvert p(a) \rvert}$.
Since $p(a)$ is a root for this equation, we have $p(a)^n + p(a)^{n-1} -\beta=0$.
I tried to use this equation to compute the condition number for $p(a)$. But I don't know I'm a right way or not.