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CA Foundation · Quantitative Aptitude · Equations

Which quadratic equation has roots that are each 2 more than the roots of x² − 5x + 6 = 0?

The equation is x² − 9x + 20 = 0. The original roots are 2 and 3, so the new roots are 4 and 5, with sum 9 and product 20. The required equation is x² − (sum)x + product = 0.

  1. Ax² − 9x + 20 = 0Correct
  2. Bx² − 7x + 12 = 0
  3. Cx² − 9x + 12 = 0
  4. Dx² + 9x + 20 = 0

Explanation

The original roots are 2 and 3, so the new roots are 4 and 5. Sum = 9 and product = 20, giving x² − 9x + 20 = 0. Option x² − 7x + 12 is the equation with roots 3 and 4, which comes from adding 1 to the roots instead of 2 mistakenly, and x² − 9x + 12 uses a wrong product.

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