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The complete solution set of inequality `((x-5)^(1005)(x+8)^(1008)(x-1))/(x^(1006)(x-2)^3(x-3)^5(x-6)(x+9)^(1010)) le 0 `

A

`(-oo,-9)cup(-8,0) cup (0,1)cup (2,3)cup [ 5,6]`

B

`(-oo,-9)cup(-9,0)cup(0,1) cup (2,3)cup [5,6)`

C

`(-oo,-9)cup (-9,0)cup (0,1] cup (2,3)cup [ 5,6)`

D

`(-oo,0) cup (0,1] cup (2,3)cup [5,6)]`

Text Solution

Verified by Experts

The correct Answer is:
C
We have `((x-5)^(1005)(x+8)^(1008)(x-1))/(x^(1006)(x-2)^3(x-3)^5(x-6)(x+9)^(1010)) le 0 `

From the sign scheme `x in (-oo ,9) cup (-9 , 0) cup (0,1) cup (2,3) cup [5,6)`
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