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SMO 2022 Senior Round 1 Question 1

SMO · SMO 2022 Senior Round 1

Question 1

Suppose the roots of $\dfrac{x^2}{2}+mx+n=0$ are $\dfrac m2$ and $\dfrac n3$. Find the smallest value of $mn$.
  1. $-1080$
  2. $-90$
  3. $0$
  4. $90$
  5. $1080$