CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
If one root of x^2 - 9x + k = 0 is twice the other root, what is the value of k?
The value of k is 18. If the roots are a and 2a, their sum 3a equals 9, so a=3 and the roots are 3 and 6. The product of the roots, which equals k, is 18.
- A9
- B12
- C18Correct
- D27
Explanation
Let roots be a and 2a. Sum: 3a=9, so a=3 and the roots are 3 and 6. Product k = 3×6 = 18. Check: x^2-9x+18=(x-3)(x-6). Choosing 27 comes from taking 3 and 9 or multiplying wrongly.
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