CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
For the equation x^2 - 6x + k = 0, one root is twice the other. What is the value of k, and what is the larger root?
k equals 8 and the larger root is 4. With roots a and 2a, the sum 3a equals 6, so a is 2. The roots are 2 and 4 and their product, which is k, equals 8.
- Ak = 8, larger root 4Correct
- Bk = 9, larger root 6
- Ck = 12, larger root 6
- Dk = 8, larger root 2
Explanation
Let roots be a and 2a. Sum 3a = 6, so a = 2 and roots are 2 and 4. Product k = 8. Check: x^2-6x+8=(x-2)(x-4). Larger root is 4, not 2.
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