The Convex Hull Of A Set Of Roots

Let $F$ denote the set of all monic polynomials $f(x)$ with complex coefficients, such that the distance between any two distinct complex roots of $[f(x)]^2-f(x)$ is at least $1$ .

For each polynomial $f$ in $F$ , let $S_f$ be the convex hull of the roots of $[f(x)]^2-f(x).$ To 2 decimal places, what is the product of the largest and the smallest possible (positive) area of $S_f$ ?