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The product of all the solutions of the ...

The product of all the solutions of the equation`(x-2)^(2)-3|x-2|+2=0` is

A

2

B

-4

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `(x-2)^(2) -3|x-2|+2 = 0`
`rArr" "|x-2|^(2) -3|x-2|+2 = 0`
`rArr" "(|x-2|-2)(|x-2|-1) = 0`
`rArr" "|x-2|=1, 2 rArr x-2 = +- 1, +- 2 rArr x = 3, 1, 4, 0`
Hence, product of roots `= 3 xx 1 xx 4 xx 0 = 0`.
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