Number of positive integers for which $$(x+3)(x$$−$$1)x2(x$$−$$2)3$$≤$$0$$ holds is

Introduction to linear inequalities

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Question

$Number of positive integers for which \frac{(x + 3) (x - 1)}{x^{2} (x - 2)^{3}} \leq 0 h o l d s i s$

Moderate

Solution

$\frac{(x + 3) (x - 1)}{x^{2} (x - 2)^{3}} \leq 0$
Sign scheme of the expression is as shown in the following figure

From the sign scheme
$x \in (- \infty, - 3] \cup [1, 2)$

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