CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
For which range of values of m does the equation x² + mx + 9 = 0 have no real roots?
No real roots means the discriminant is negative: m² − 4(1)(9) < 0, so m² < 36. This gives −6 < m < 6. The outside range, m below −6 or above 6, would give two distinct real roots instead.
- A−6 < m < 6Correct
- Bm < −6 or m > 6
- C−3 < m < 3
- Dm > 6 only
Explanation
No real roots requires D < 0: m² − 36 < 0, so m² < 36, giving −6 < m < 6. Option 2 is the range for real roots (D > 0), the opposite condition. Option 3 uses m² < 9, from forgetting the factor 4.
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