Mathematics 2012 JAMB Past Questions - Question 17: Find the range of values of m which satisfy (m-3)(m-4)

Correct Answer

C

Explanation

(m-3) (m-4) < 0m-3 < 0; m - 4 < 0m < 3; m < 43 < m < 4To find the range of values of m that satisfy the inequality (m-3)(m-4) < 0, we can use the concept of interval notation.First, let's find the critical points by setting each factor equal to zero:m - 3 = 0 => m = 3m - 4 = 0 => m = 4These critical points divide the number line into three intervals: (-∞, 3), (3, 4), and (4, +∞).Next, we can test a value from each interval to determine the sign of the expression (m-3)(m-4) within that interval.For the interval (-∞, 3), we can choose m = 0:(0-3)(0-4) = (-3)(-4) = 12 > 0For the interval (3, 4), we can choose m = 3.5:(3.5-3)(3.5-4) = (0.5)(-0.5) = -0.25 < 0For the interval (4, +∞), we can choose m = 5:(5-3)(5-4) = (2)(1) = 2 > 0From these tests, we can see that the expression (m-3)(m-4) is negative (less than zero) in the interval (3, 4).Therefore, the range of values of m that satisfy the inequality (m-3)(m-4) < 0 is m ∈ (3, 4).