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SMO 2006 Senior Round 1 Question 9

SMO · SMO 2006 Senior Round 1

Question 9

Suppose $a,b,c$ are real numbers such that $a+b+c=0$ and $abc=-100$. Let $x=\dfrac1a+\dfrac1b+\dfrac1c$. Which statement is true?
  1. $x\gt 0$
  2. $x=0$
  3. $-1\lt x\lt 0$
  4. $-100\lt x\lt -1$
  5. $x\lt -100$