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

The supremum of |{x ∈ ℝ : |f x| < 1}| over all monic polynomials f such that all of its roots are real and contained in [-1,1] is 2 * 2 ^ (1 / 2). This is proved in [Tao25].