Question 76
Let $P_1(x) = a x^2 - b x - c$, $P_2(x) = b x^2 - c x - a$, $P_3(x) = c x^2 - a x - b$ be three quadratic polynomials where $a$, $b$, $c$ are non-zero real numbers. Suppose there exists a real number $\alpha$ such that $P_1(\alpha) = P_2(\alpha) = P_3(\alpha)$. Prove that $a = b = c$.