Set of real numbers | TOMATO B.Stat Objective 714

The set of all real numbers x satisfying the inequality \(x^{3}(x+1)(x-2) \geq 0\) can be written as

\(x^{3}(x+1)(x-2) \geq 0\)

case I \(x^{3}(x+1)(x-2) \geq 0\)

or, \(0 \leq x, -1 \leq x, 2 \leq x\) which is first inequation

case II \(x^{3} \geq 0, (x+1) \leq 0, (x-2) \leq 0\)

or, \(x \geq 0, x \leq -1, x \leq 2\) which is second equation

case III \(x^{3} \leq 0, (x+1) \leq 0, (x-2) \geq 0\)

or, \(x \leq 0 x \leq -1, 2 \leq x\) which is third equation

case IV \(x^{3} \leq 0, (x+1) \geq 0, (x-2) \leq 0\)

or, \(x \leq0, x \geq -1, x \leq 2\) which is fourth equation

Combining we get \(x^{3}(x+1)(x-2) \geq 0\) satisfy if \(x\in\) \([-1,0] \bigcup [2,infinity)\)

or, answer option none of these

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