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For real solution of equation 3sqrt(x+3p...

For real solution of equation `3sqrt(x+3p+1)-3sqrt(x)=1`, we have

A

`p ge 1//4`

B

`p ge -1//4`

C

`p ge 1//3`

D

`p ge -1//3`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `3sqrt(x+3p+1)=3sqrt(x)+1`
Let `3sqrt(x)=h`
`implies3sqrt(x+3p+1)=h+1`
`impliesx+3p+1=h^(3)+3h^(2)+3h+1`
`implies h^(3)+3p+1=h^(3)+3h^(2)+3h+1`
`implies3h^(2)+3h-3p=0`
`h^(2)+h-p=0`
For real roots ` D ge 0`
`implies 1+4p ge 0`
`implies p ge -1//4`
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