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CA Foundation · Quantitative Aptitude · Equations

Which of the following is a root of the cubic equation x³ − 6x² + 11x − 6 = 0?

The root is x = 2. Substituting 2 gives 8 − 24 + 22 − 6 = 0, so the equation is satisfied. The other values 4, −1 and 5 give 6, −24 and 24 respectively, so none of them is a root.

  1. Ax = 4
  2. Bx = 2Correct
  3. Cx = −1
  4. Dx = 5

Explanation

Put x = 2: 8 − 24 + 22 − 6 = 0, so x = 2 satisfies the equation. For x = 4: 64 − 96 + 44 − 6 = 6, not zero. For x = −1: −1 − 6 − 11 − 6 = −24. For x = 5: 125 − 150 + 55 − 6 = 24. Only x = 2 works.

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