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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

  1. either the empty set or the set of all integers
  2. the set of all integers
  3. the set of all positive integers
  4. the empty set
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