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
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 \(x^{3}(x+1)(x-2) > 0\)
or, \(0<x, -1<x, 2<x\) which is first inequation
case II \(x^{3}>0, (x+1)<0, (x-2)<0\)
or, \(x>0, x<-1, x<2\) which is second equation
Second Hint
case III \(x^{3}<0, (x+1)<0, (x-2)>0\)
or, x<0 x<-1, 2<x which is third equation
case IV \(x^{3}<0, (x+1)>0, (x-2)<0\)
or, x<0, x>-1, x<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, noneof these.
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