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CA Foundation · Quantitative Aptitude · Equations

For the cubic equation x³ − 7x + 6 = 0, what is the sum of the squares of its roots?

The sum of the squares of the roots is 14. The roots are 1, 2 and −3, whose squares 1, 4 and 9 add to 14. The identity (sum)² − 2×(pairwise product sum) = 0 − 2(−7) gives the same result.

  1. A14Correct
  2. B49
  3. C7
  4. D12

Explanation

The roots are 1, 2 and −3 (check: 1 − 7 + 6 = 0; 8 − 14 + 6 = 0; −27 + 21 + 6 = 0). Their squares are 1, 4 and 9, summing to 14. Using the identity (sum)² − 2(sum of pairwise products) = 0 − 2(−7) = 14. Option 7 forgets to multiply by 2.

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