Question 66
Let $k$ be a real number such that the product of real roots of the equation
$$
X^{4}+2 X^{3}+(2+2 k) X^{2}+(1+2 k) X+2 k=0
$$
is $-2013$. Find the sum of the squares of these real roots.
$$
X^{4}+2 X^{3}+(2+2 k) X^{2}+(1+2 k) X+2 k=0
$$
is $-2013$. Find the sum of the squares of these real roots.