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Sendov's conjecture states that if all the zeroes of a complex polynomial$P(z)$ of degree at least two lie in the unit disk, then within a unit distanceof each zero lies a critical point of $P(z)$. In a paper that appeared in 2014,D\'{e}got proved that, for each $a\in (0,1)$, there exists an integer $N$ suchthat for any polynomial $P(z)$ with degree greater than $N$, if $P(a) = 0$ andall zeroes lie inside the unit disk, the disk $|z-a|\leq 1$ contains a criticalpoint of $P(z)$. Based on this result, we derive an explicit formula$\mathcal{N}(a)$ for each $a \in (0,1)$ and, consequently obtain a uniformbound $N$ for all $a\in [\alpha , \beta]$ where $0<\alpha < \beta < 1$. This(partially) addresses the questions posed in D\'{e}got's paper.

Sendov's Conjecture: A note on a paper of D\'{e}got