Smale's mean-value conjecture for polynomial critical points

Let $p$ be a polynomial of degree $n$ with $p(0)=0$ and $p'(0)\neq0$. Smale's conjecture. At least one root $\mu_j$ of $p'$ satisfies

$$\frac{p(\mu_j)}{\mu_j}\leq p'(0).$$

The source lists this among open conjectures in the geometry of polynomials and gives no resolution.