Question 42
Let $a$, $b$, $c$, $d$ be real numbers such that $b - d \ge 5$ and all zeros $x_1$, $x_2$, $x_3$, and $x_4$ of the polynomial $P(x) = x^4 + a x^3 + b x^2 + c x + d$ are real. Find the smallest value the product $(x_1^2 + 1)(x_2^2 + 1)(x_3^2 + 1)(x_4^2 + 1)$ can take.