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The equation ||x-2|+a|=4 can have four d...

The equation `||x-2|+a|=4` can have four distinct real solutions for `x` if `a` belongs to the interval
a) `(-oo,-4)`
(b) `(-oo,0)`
c) `(4,oo)`
(d) none of these

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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