1.

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

Answer»

`(-OO,0)`
`(-1,(-2)/(3))`
`(-oo,(-2)/(3))`
`(-1,oo)`

Solution :`(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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