Erdős problem 1038 · problems.science

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