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

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)

Equation

Roots

Algebra

But try the problem first...

Answer:none of these

Source

Suggested Reading

B.Stat Objective Problem 714

Challenges and Thrills of Pre-College Mathematics by University Press

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

- https://www.cheenta.com/gcd-and-bezout-theorem/
- https://www.youtube.com/watch?v=w0Y2oXoyEEQ&t=6s
- Our BStat-BMath Program for ISI and CMI Entrance

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