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
Equation
Roots
Algebra
But try the problem first...
Answer:none of these
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
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