Multiple choice

If $\displaystyle \alpha$, $\displaystyle \beta$, $\displaystyle \gamma$ are the roots of the equation $\displaystyle x^{3} + qx + r = 0$, then the equation whose roots are $\displaystyle \frac{\beta + \gamma}{\alpha^{2}}, : \frac{\gamma + \alpha}{\beta^{2}}, : \frac{\alpha + \beta}{\gamma^{2}}$, is

  1. $\displaystyle rx^{3} + qx^{2} + 1 = 0$
  2. $\displaystyle rx^{3} - qx^{2} - 1 = 0$
  3. $\displaystyle qx^{3} + rx^{2} + 1 = 0$
  4. $\displaystyle qx^{3} - rx^{2} - 1 = 0$
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B Correct answer
Explanation

This is a standard transformation of roots for the cubic equation x^3 + qx + r = 0. The transformation leads to rx^3 - qx^2 - 1 = 0.

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