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Erdős problem 1038

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Among all nonconstant monic polynomials ff whose roots lie in [−1,1][-1, 1], determine inf⁡f∣{x∈R:∣f(x)∣<1}∣\inf_f |\{x \in \mathbb{R} : |f(x)| < 1\}|.

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Among all nonconstant monic polynomials $f$ whose roots lie in $[-1, 1]$, determine $\inf_f |\{x \in \mathbb{R} : |f(x)| < 1\}|$.

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