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CA Foundation · Quantitative Aptitude · Equations

If the roots of x² − 8x + 15 = 0 are α and β, which quadratic equation has roots α + 1 and β + 1?

The required equation is x² − 10x + 24 = 0. The original roots are 3 and 5, so the new roots are 4 and 6, with sum 10 and product 24. The product must be recomputed, not kept at 15.

  1. Ax² − 10x + 24 = 0Correct
  2. Bx² − 8x + 24 = 0
  3. Cx² − 10x + 15 = 0
  4. Dx² − 10x + 23 = 0

Explanation

α + β = 8 and αβ = 15 (roots 3 and 5). New roots 4 and 6: sum = 10, product = 24. The equation is x² − 10x + 24 = 0. Option x² − 10x + 15 keeps the old product, which is wrong because the product changes to αβ + (α + β) + 1 = 24.

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