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If |x^2-2x+2|-|2x^2-5x+2|=|x^2-3x| then ...

If `|x^2-2x+2|-|2x^2-5x+2|=|x^2-3x|` then the set of values of x is

A

a.`(-oo , 0] cup [ 3,0)`

B

b.`[0,1/2] cup [2,3]`

C

c.`(-oo,0]cup [1/2,2] cup [3,oo)`

D

d.`[0,2] cup [3,oo)`

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`|2x^(2)-5x+2|+|x^(2)-3x|=|x^(2)-2x+2| = |(2x^(2)-5x+2)-(x^(2)-3x)|`
`therefore (2x^(2)-5x+2) (x^(2)-3x) le 0`
`rArr (2x-1) (x-2) x (x-3) le 0`

From the sign scheme, we have `x in[0,(1)/(2)]cup [2,3]`
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