CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
The roots of 3x² − 12x + (k + 1) = 0 are real and distinct, and k is a positive integer. What is the greatest possible value of k?
The discriminant is 144 − 12(k + 1), which must be positive for distinct real roots. That gives k + 1 < 12, so k < 11. The largest positive integer value is 10, since k = 11 makes the roots equal.
- A10Correct
- B11
- C12
- D13
Explanation
D = 144 − 12(k + 1) > 0, so k + 1 < 12, meaning k < 11. The greatest positive integer is 10. At k = 11, D = 0 and the roots would be equal, not distinct, so 11 is wrong. Options 12 and 13 give negative D.
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