MathNet 2009-part-05 — 172 problems (EN–VI) Question 88

Let $f(x) = x^{4} + 14 x^{3} + 52 x^{2} + 56 x + 16$. Let $z_{1}, z_{2}, z_{3}, z_{4}$ be the four roots of $f$. Find the smallest possible value of $\left|z_{a} z_{b} + z_{c} z_{d}\right|$ where $\{a, b, c, d\} = \{1,2,3,4\}$.