The roots of the equation |2x−1|2−3|2x−1|+2=0 are

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−12,0,12

-12,0,32

-32,12,0,1

-12,0,1,32

answer is D.

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Detailed Solution

Given equation is|2x-1|2-3|2x-1|+2=0Let |2 x-1|=t∴ t2-3t+2=0⇒ (t-1)(t-2)=0⇒t=1,2 ⇒ |2x−1|=1 and |2x−1|=2⇒ 2x−1=±1 and 2x−1=±2⇒ x=1,0 and x=32,−12

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