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CA Foundation · Quantitative Aptitude · Equations

Which of the following is the set of values of x satisfying x² − 5x − 14 = 0?

The roots are x = 7 and x = −2. The equation factorises as (x − 7)(x + 2) = 0, since the roots must add up to 5 and multiply to −14, which 7 and −2 do.

  1. Ax = 7 and x = −2Correct
  2. Bx = −7 and x = 2
  3. Cx = 7 and x = 2
  4. Dx = −7 and x = −2

Explanation

Factorise: x² − 5x − 14 = (x − 7)(x + 2) since 7 × (−2) = −14 and 7 + (−2) = 5, matching the middle term −5x only after sign check: −7 + 2 = −5 in the factors (x − 7)(x + 2). Roots are 7 and −2. Check: sum 5, product −14. The pair −7 and 2 has sum −5, so it is wrong.

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