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

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.