Multiple choice

lf $\alpha,\beta,\gamma$ are the roots of $x^{3}+2x-3=0$, then the transformed equation having the roots $ \displaystyle \frac{\alpha}{\beta}+\frac{\beta}{\alpha},\frac{\beta}{\gamma}+\frac{\gamma}{\beta},\frac{\gamma}{\alpha}+\frac{\alpha}{\gamma}$ is obtained by taking $x=$

  1. $\displaystyle \frac{3}{2}(1-y)$
  2. $-\displaystyle \frac{3}{2}(1+y)$
  3. $3(1-y)$
  4. $3(1+y)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a pair of roots a and b, the transformed value is a/b + b/a = c^3/3 - 2, where c is the remaining root and abc = 3. Since c^3 + 2c - 3 = 0, this becomes -1 - 2c/3, so c = -3/2(1 + y).

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