CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
If the roots of x² + (m − 2)x + 9 = 0 are equal and m is positive, what is the value of m?
The value of m is 8. Equal roots need the discriminant (m − 2)² − 4(1)(9) to be zero, so m − 2 = ±6, giving m = 8 or −4. Because m is stated to be positive, only 8 is valid.
- A8Correct
- B−4
- C4
- D6
Explanation
Equal roots need (m − 2)² − 36 = 0, so m − 2 = ±6, giving m = 8 or m = −4. Since m is positive, m = 8. The value −4 is rejected as it is negative; 4 and 6 do not satisfy the condition.
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