Question

(1) If f(x) is a non-constant polynomial satisfying 27f(x^3)−4f(x^2)−x^6f(3x)+46=0, what is f(2)?

(2) a,b and c are positive integers such that f(x)=ax^2−bx+c has 2 distinct real roots α and β that satisfy the strict inequality 0<α<β<1. What is the minimum value of a?