CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
For which value of k does the equation x² − 6x + k = 0 have two equal roots?
The value is k = 9. Equal roots require the discriminant b² − 4ac to be zero, so 36 − 4k = 0 and k = 9. The equation then becomes (x − 3)² = 0 with the repeated root 3.
- A9Correct
- B6
- C3
- D36
Explanation
Equal roots need discriminant = 0: 36 − 4k = 0, so k = 9. Then x² − 6x + 9 = (x − 3)², with the repeated root 3. The option 36 comes from forgetting to divide by 4.
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