If one root of the equation x^{2}-kx+k=0 exceeds the other by 2\sqrt{3}, then which one of the following is a value of k?
- A. 3
- B. 6 ✓
- C. 9
- D. 12
Correct Answer: B. 6
Explanation
Let roots be \alpha and \beta. Difference is 2\sqrt{3}. (\alpha - \beta)^2 = (\alpha+\beta)^2 - 4\alpha\beta = k^2 - 4k = 12. Solving k^2 - 4k - 12 = 0 gives k = 6 or -2.
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