**Sendov's conjecture** states that for a polynomial
$$f(z)=(z-r_{1})\cdots (z-r_{n}),\qquad (n\geq 2)$$
with all roots $r_1, ..., r_n$ inside the closed unit disk $|z| ≤ 1$, each of the $n$ roots is at a
distance no more than $1$ from at least one critical point.
It has been shown that Sendov's conjecture holds when the degree of $n$ is at most $9$.
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