Doubt from Theory of equations

It's b or c..Is it multiple correct?

Option c is given. Can you explain?

Any root of the cubic should not lie in the range of quadratic for the 2nd eq to have no roots. So, the roots of cubic can be integers less than 1.
Then use sum of roots of cubic to find 'a' which can only be positive for integral roots less than 1 and also can't be 2 as sum of any three integral roots less than 1 can't give -2 which leaves us with option c only.