CA Foundation · Quantitative Aptitude · Equations
For which value of k will the equation x² − 7x + k = 0 have roots whose difference is 3?
The value of k is 10. The roots sum to 7 and differ by 3, so they are 5 and 2. Their product, 5 × 2 = 10, equals k, and the equation becomes x² − 7x + 10 = 0.
- A8
- B10Correct
- C12
- D14
Explanation
Let roots be a and b with a + b = 7 and a − b = 3. Then a = 5 and b = 2. The product is 5 × 2 = 10 = k. Check: (x − 5)(x − 2) = x² − 7x + 10, and the difference is 3. The value 12 would come from roots 3 and 4, whose difference is only 1.
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