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The set of all values of x for which (...

The set of all values of `x` for which
`((x+1)(x-3)^(2)(x-5)(x-4)^(3)(x-2))/(x) lt 0`

A

`(-oo,-1) uu (0,2) uu (4,5)`

B

`(-1,0) uu (2,4) uu (5,oo)`

C

`(-1,0) uu (2,3) uu (4,5)`

D

`(-oo,-1) uu (0,2) uu [3,5)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` We have `E=((x+1)(x-3)^(2)(x-5)(x-4)^(3)(x-2))/(x)`
Sign scheme of `E` is as shown below.

At `x=3`, sign of the expression does not change as `(x-3)` has power `'2'`.
`x in(-oo,-1)uu(0,2)uu(4,5)`
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