CA Foundation · Quantitative Aptitude · Equations
If the roots of the quadratic equation x² − 7x + k = 0 differ by 1, what is the value of k?
The value of k is 12. With roots differing by 1 and summing to 7, the roots are 3 and 4, and their product is 12. This equals k, since the product of roots in x² − 7x + k is k.
- A10
- B12Correct
- C14
- D6
Explanation
Let the roots be a and a+1. Sum = 2a+1 = 7, so a = 3 and the roots are 3 and 4. Product = 12, so k = 12. Check: (4−3)² = 49 − 4×12 = 1. The value 10 would come from wrongly taking roots 2 and 5, which differ by 3.
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