Let f(x)=x2−ax+b, where a and b are positive integers.
(a) Suppose that a=2 and b=2. Determine the set of real roots of f(x)−x, and the set of real roots of f(f(x))−x.
(b) Determine the number of positive integers (a,b) with 1≤a,b≤2011 for which every root of f(f(x))−x is an integer. algebrapolynomialquadratics