USAMO 2014 — Days 1 and 2 Question 1

Let $a,b,c,d$ be real numbers such that $b-d\ge5$ and all four zeros $x_1,x_2,x_3,x_4$ of $P(x)=x^4+ax^3+bx^2+cx+d$ are real. Find the minimum of $(x_1^2+1)(x_2^2+1)(x_3^2+1)(x_4^2+1)$.

Proposed by Titu Andreescu (as credited in the supplied compilation).