Maths Core Pure AS Series question

Question and images below

My question is about part b)

The solution is here:

I understood everything from the solution until the last two lines about the discriminant not being a square. Why does the discriminant not being a square mean there are no values of n that (blah blah blah)? Is it because a non-square discriminant gives a decimal (non-integer)? That wouldn’t make sense because let’s say hypothetically you plug in 4, a square number- that would still give you a decimal, so why does the discriminant being non-square mean there are no values of n that (blah blah blah)?

Duplicate post. As I tried to hint at, the discirimiant being square is a necessary but not sufficient condition for n being an integer. As per the other thread, why not simply work through the quadratic formula parts (-b +/-sqrt(discriminant))/2a, with a few values if necessary, and think about when it evaluates to an integer or not.

i dont think this is AS