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

Question

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

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)`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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))`

4 views Answered 2023-02-05 15:29