The equation `2^(2x) + (a - 1)2^(x+1) + a = 0` has roots of opposite
sing, then exhaustive set of values of a is

Options

A. ` a in (- 1, 0 )`
B. `a lt 0`
C. ` a in (-infty, 1//3)`
D. ` a in (0, 1//3)`

Answer

3

Explanation

The given equation is
`2^(2x) + (a - 1) 2^(x+1)+ a = 0 `
or ` t^(2) + 2(a - 1) t + a = 0 ` where `2^(x) = t`
Now, t = 1 should lie between the roots of this equation
` therefore 1 + 2(a - 1) + a lt 0 oe a lt (1)/(3)` .