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Q.

The roots of |x-2|2+|x-2|-6=0 are

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a

0, 4

b

-1, 3

c

4, 2

d

5, 1

answer is A.

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Detailed Solution

When x<2, (x-2)2-(x-2)-6=0⇒x2 -4x+4-x+2-6=0⇒x2-5x=0 ⇒x(x-5)=0⇒x=0When x≥2; (x-2)2+(x-2)-6=0⇒x2-4x+4+x-2-6=0 ⇒x2-3x-4=0⇒x2-4x+x-4=0 ⇒(x-4)(x+1)=0⇒x=4.

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