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If the equation 2^(2x)+a*2^(x+1)+a+1=0 h...

If the equation `2^(2x)+a*2^(x+1)+a+1=0` has roots of opposite sign, then the exhaustive set of real values of `a` is

A

`(-oo,0)`

B

`(-1,(-2)/(3))`

C

`(-oo,(-2)/(3))`

D

`(-1,oo)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` Put `2^(x)=t`
`implies t^(2)+2a*t+(a+1)=0`
Now, `t=1` should lie between the roots of above equation.
Let `f(t)=t^(2)+2a*t+(a+1)`
`:.f(1) lt 0` and `f(0) gt 0`
`implies a lt (-2)/(3)` and `a gt -1`
`:.a in (-1,(-2)/(3))`
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