Question
Question: Complete solution set of the inequality x(e<sup>x</sup> – 1)(x + 2)(x – 3)<sup>2</sup> \< 0 is...
Complete solution set of the inequality x(ex – 1)(x + 2)(x – 3)2 < 0 is
A
[-2, 3]
B
(-2, 0]
C
(-∞, -2] ∪ {0, 3}
D
(-∞,-2] ∪ [0, 3]
Answer
(-∞, -2] ∪ {0, 3}
Explanation
Solution
Using wavy curve method and the fact that x = 0 and 3 are the repeated roots of x(ex - 1) (x + 2) (x - 3)2 = 0, we get the sign scheme of the given expression as
Thus complete solution is x∈ (-∞, -2] ∪ {0, 3}.