If S is the set of all real x such that ...

If S is the set of all real `x` such that `(2x-1)/(2x^3+3x^2+x)` is `(-oo,-3/2)` b. `(-3/2,1/4)` c. `(-1/4,1/2)` d. `(1/2,3)` e. None of these

A

`(-infty,-(3)/(2))`

B

`(-(3)/(2),(1)/(4))`

C

`(-(1)/(4),(1)/(2))`

D

`((1)/(2),3)`

Text Solution

Verified by Experts

The correct Answer is:

A, D

`(2x-1)/(2x^(3)+3x^(2)+x)ge0implies(2x-1)/(x(2x^(2)+3x+1))ge0`
`implies(2x-1)/(x(2x+1)(x+1))ge0`
`implies x in (-infty,-1)cup(-(1)/(2),0)cup((1)/(2),infty)`

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