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CA Foundation · Quantitative Aptitude · Equations

The roots of x² − 5x + 6 = 0 are α and β. Which quadratic equation has roots α² and β²?

The equation is x² − 13x + 36 = 0. The original roots are 2 and 3, so the new roots are 4 and 9, with sum 13 and product 36.

  1. Ax² − 13x + 36 = 0Correct
  2. Bx² − 25x + 36 = 0
  3. Cx² − 13x + 6 = 0
  4. Dx² + 13x + 36 = 0

Explanation

Roots are 2 and 3. The new roots are 4 and 9. Sum = 13 and product = 36, so the equation is x² − 13x + 36 = 0. The option with 25 squares the sum instead of using α² + β². The option with 6 uses the old product instead of squaring it.

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