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This problem trains for: AMC-10, AMC-12, Math Kangaroo 9-10.

What are the possible values of the parameter m so that the equation below will have exactly one positive real root smaller than 1?

For the function to have exactly one real root in some interval, it is necessary and sufficient for its graph to intersect the x-axis only once in that interval. This is equivalent to saying that the function must change sign once over the specified interval:

which can be further applied to the given equation as follows:

The correct answer is E.