Modification and confusion

Decleration of q, r are unreal is too jump. However, the coeficiants of (x-q)(x-q) can be represented by a, once this quadratic equation does not have real root, the value of f(0) is allowed.

Now, I am confused.

Given complex number f(0), by rule in case 1, we have a, b and one (x-q)(x-r)=I. On the other hand, by rule in case 2, we get another (x-q)(x-r)=II. If only one of them have two unreal roots, the value of f(0) is allowed or not allowed? Since the allowed and not allowed is contradiction, does that means I and II should both have the same number of real root (0 or 1). No interest for too complicated calculation,do not know the real format ot I and II.

Accept complex number, the exercise becomes a paper.