Let $k$ be a real number such that the product of real roots of the equation $$X^4 + 2X^3 + (2 + 2k)X^2 + (1 + 2k)X + 2k = 0$$is $-2013$. Find the sum of the squares of these real roots.
Source: 2013 Saudi Arabia BMO TST I p5
Tags: polynomial, roots, algebra
Let $k$ be a real number such that the product of real roots of the equation $$X^4 + 2X^3 + (2 + 2k)X^2 + (1 + 2k)X + 2k = 0$$is $-2013$. Find the sum of the squares of these real roots.