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The number of roots of the equation 2|x|...

The number of roots of the equation `2|x|^(2) - 7|x| + 6 = 0`

A

4

B

3

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
`2|x|^(2) - 7 |x| + 6 = 0`
Let `|x | = y `
`2y^(2) -7y + 6 = 0`
`2y^(2) - 3y - 4 y + 6 = 0`
`y(2y-3)-2(2y+3) = 0`
`(2y-3)(y-2) = 0`
`2y-3=0` or `y-2= 0`
`y = 3/2` or `y = 2`.
`|x| = 3/2` or `|x| = 2`
`x = +- 3/2` or `x = +-2`
`:.` x has `4` real solutions.
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