Puzzle 48 - Roots of a cubic

From Rolle’s theorem, we can conclude that between every pair of distinct roots of a polynomial P(x), there lies a root of its derivative P’(x). If P’(x) keeps its sign unchanged between any two distinct real numbers, then it is possible that P(x) does not have a root between them and hence may keep the same sign between those real numbers. Further if P(x) has two equal roots, then it will have a common root with its derivative. Consider with being an integer between and both inclusive, then find the number of values of if has to have
(i) one real root and two complex roots, (ii) only two equal roots