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Let $a, b, c$ be non-zero real numbers such that $b^{2}<4 a c$, and $f(x)=a x^{2}+b x+c$. If the set $S$ consists of all integers $m$ such that $f(m)<0$, then the set $S$ must necessarily be

- either the empty set or the set of all integers
- the set of all integers
- the set of all positive integers
- the empty set