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CA Foundation · Quantitative Aptitude · Equations

If α and β are the roots of x² − 5x + 3 = 0, which equation has roots α/β and β/α?

The required equation is 3x² − 19x + 3 = 0. The new roots have sum (α² + β²)/αβ = 19/3 and product 1, so the equation is x² − (19/3)x + 1 = 0, which multiplies out to 3x² − 19x + 3 = 0.

  1. A3x² − 19x + 3 = 0Correct
  2. B3x² − 25x + 3 = 0
  3. Cx² − 19x + 3 = 0
  4. D3x² + 19x + 3 = 0

Explanation

α + β = 5 and αβ = 3. Sum of new roots = (α²+β²)/(αβ) = (25 − 6)/3 = 19/3. Product = 1. The equation is x² − (19/3)x + 1 = 0, i.e. 3x² − 19x + 3 = 0. Option 2 uses 25 and forgets the −2αβ.

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