Question 55
Let $x_1 \le x_2 \le x_3 \le x_4$ be four real numbers. Prove that there exist polynomials $P(x)$ and $Q(x)$ of degree two with real coefficients such that $x_1, x_2, x_3$ and $x_4$ are the roots of $P(Q(x))$ if and only if $x_1 + x_4 = x_2 + x_3$.