JAMB Mathematics 2012 Paper

Concept:For a product of two factors to be negative, one factor must be positive and the other negative.Explanation:The critical points are found when each factor equals zero:$m - 3 = 0 \Rightarrow m = 3$$m - 4 = 0 \Rightarrow m = 4$These points divide the number line into three intervals:$m < 3$, $3 < m < 4$, and $m > 4$.Test a value in each interval.For $m < 3$, take $m = 2$: $(2 - 3)(2 - 4) = (-1)(-2) = +2 > 0$.For $3 < m < 4$, take $m = 3.5$: $(3.5 - 3)(3.5 - 4) = (0.5)(-0.5) = -0.25 < 0$.For $m > 4$, take $m = 5$: $(5 - 3)(5 - 4) = (2)(1) = +2 > 0$.The inequality holds only when $3 < m < 4$.Answer:$3 < m < 4$Correct option: C.