CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
The equation x² − 6x + k = 0 has two equal real roots. What is the value of k, and what is the repeated root?
For equal roots the discriminant must be zero, so 36 − 4k = 0 and k = 9. The equation is then (x − 3)² = 0, so the repeated root is 3. The sum of roots is 6, split equally as 3 and 3.
- Ak = 9, root = 3Correct
- Bk = 9, root = 6
- Ck = 6, root = 3
- Dk = 36, root = 3
Explanation
Equal roots need D = 0: 36 − 4k = 0, so k = 9. The equation becomes (x − 3)² = 0, giving root 3 repeated. Root 6 confuses the sum of roots with each root; k = 36 forgets the factor 4 in 4ac.
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