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CA Foundation · Quantitative Aptitude · Equations

What is the sum of all the roots of the cubic equation x³ − 6x² + 11x − 6 = 0?

The sum of the roots is 6. For a cubic ax³ + bx² + cx + d = 0 the sum of the roots equals −b/a, which here is 6. The equation factors with roots 1, 2 and 3, confirming the total of 6.

  1. A6Correct
  2. B11
  3. C−6
  4. D−11

Explanation

For a cubic ax³ + bx² + cx + d = 0, the sum of the roots is −b/a. Here b = −6 and a = 1, so the sum is 6. Check: the roots are 1, 2 and 3, which add up to 6. The value 11 is the sum of products of roots taken two at a time, not the sum of roots.

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