If the equation \((m - 3)x^2 - 2mx + 5m = 0\) has real and positive roots, then the possible value(s) of m lies in:
Question and options
If the equation has real and positive roots, then the possible value(s) of m lies in:
- [2,3]
- (2,3.8)
- (3, 3.75]
- [3.1, 4)
Answer and explanation
Correct answer: C - (3, 3.75]
Real roots: D = 4m^2 - 20m(m-3) = 4m(15-4m) >= 0 -> 0 <= m <= 3.75. Positive roots need sum 2m/(m-3) > 0 and product 5m/(m-3) > 0, so m > 3. Hence m in (3, 3.75].
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