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Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Set of real numbers.

## Set of real Numbers (B.Stat Objective Question )

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

• [-1,infinity)
• none of these
• [2,infinity)
• [0,infinity)

### Key Concepts

Equation

Roots

Algebra

But try the problem first…

Source

B.Stat Objective Problem 714

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

First hint

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

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

Second Hint

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

Final Step

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