Mathematics 2017 JAMB Past Questions - Question 18: solve (x-3) (x+2) < 0

Correct Answer

C

Explanation

To solve the inequality (x-3)(x+2) < 0, we can use the method of intervals.First, we find the critical points by setting each factor equal to zero and solving for x:x - 3 = 0 => x = 3x + 2 = 0 => x = -2Now, we can plot these critical points on a number line and test the intervals between them to see where the inequality is satisfied.We have three intervals to test: (-∞, -2), (-2, 3), and (3, ∞).For the interval (-∞, -2), we choose x = -3:(-3 - 3)(-3 + 2) = (-6)(-1) = 6, which is not less than 0.For the interval (-2, 3), we choose x = 0:(0 - 3)(0 + 2) = (-3)(2) = -6, which is less than 0.For the interval (3, ∞), we choose x = 4:(4 - 3)(4 + 2) = (1)(6) = 6, which is not less than 0.So, the solution to the inequality (x-3)(x+2) < 0 is -2 < x < 3.