CA Foundation · Quantitative Aptitude · Equations
The equation x³ − 6x² + 11x − 6 = 0 has three integer roots. What is the sum of the squares of its roots?
The sum of squares of the roots is 14. The sum of roots is 6 and the sum of pairwise products is 11, so the sum of squares is 36 − 22 = 14. This matches the roots 1, 2 and 3, whose squares add to 14.
- A14Correct
- B36
- C25
- D12
Explanation
Sum of roots = 6 and sum of products taken two at a time = 11. Sum of squares = 6² − 2(11) = 36 − 22 = 14. Check: the roots are 1, 2, 3 and 1 + 4 + 9 = 14. The value 36 ignores the subtraction of twice the pair-product sum.
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