CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
The roots of x² − 9x + k = 0 differ by 3 (the roots are real). What is the value of k?
The value of k is 18. The roots sum to 9 and differ by 3, so they are 6 and 3. The constant term equals the product of the roots, 6 × 3 = 18. Option 20 does not match any pair of roots satisfying both conditions.
- A16
- B18
- C20Correct
- D24
Explanation
Sum of roots = 9 and difference = 3, so the roots are (9+3)/2 = 6 and (9−3)/2 = 3. Then k = product = 6 × 3 = 18. Check: 6+3 = 9 and 6−3 = 3, so it reconciles. Hence the correct value is 18, and option 20 is wrong.
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