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Set of real numbers | TOMATO B.Stat Objective 714

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Set of real numbers. You may use sequential hints.

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

Check the Answer


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

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

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