Question 6
Determine whether there exist two distinct finite subsets $A$ and $B$ of the reals such that for every polynomial $f$ of degree $2012$ with real coefficients,
$$
\sum_{x \in A} f(x) = \sum_{x \in B} f(x)
$$
$$
\sum_{x \in A} f(x) = \sum_{x \in B} f(x)
$$