AS maths Core Pure Series question

My question is about part b)

This is the solution


I understood the whole of the solution until the last 2 lines where it talked about the discriminant not being a square. Why would that mean there are no values of n that satisfy blah blah blah(the question)? Is it because the discriminant not being a square would give a decimal (not an integer), hence proving there are no values of n that…(blah blah blah)? But hypothetically even if we had a square number, say 16, that would still give decimal values of n. So why/how does the discriminant not being a square prove the question?

Why not just try it yourself, so what is n using the usual quadratic formula?
If the discriminant is not a square, what does it tell you?
What are the necessary conditions for n to be an integer using the quadratic formula?

Just found this after looking at your profile, I appreciate your help. So the necessary conditions for n to be an integer would be 1) square discriminant and 2) the values of the square root of the discriminant, when added or substrates to negative b divided by 2a, must also be rational numbers