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MathNet 2026 — Part 07 Question 89

Math Olympiad Vault · MathNet 2026 — Part 07

Question 89

Which of the following quadratic expressions in $x$ have roots $\frac{g}{h}$ and $-\frac{h}{g}$?
  1. $g^{2} h^{2} x^{2}-\frac{g^{2}}{h^{2}}$
  2. $h g x^{2}+\left(g^{2}-h^{2}\right) x-h g$
  3. $h g x^{2}+\left(h^{2}-g^{2}\right) x+h g$
  4. $h g x^{2}+\left(h^{2}-g^{2}\right) x-h g$