Existence, Uniqueness and Counterexamples · Medium problem

True: $n = 2.5$ makes it negative

False: $n^2 - 5n + 6 = (n - 2)(n - 3)$ is negative only strictly between $2$ and $3$, where there are no integers

False: $n = 0$ gives $6$, which is positive

True: $n = 2$ gives $0$