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Find the values of a for which the equat...

Find the values of `a` for which the equation `||x-2|+a|=4` can have four distinct real solutions.

A

`(-oo, -4)`

B

`(-oo,0]`

C

`[4,oo)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`|x-2|+a=+-4`
`or |x-2|= +-4-a`
For four real roots,
`4-a gt 0 and -4 -a gt 0`
` or a in (-oo, -4)`
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