Which of the following is correct for the equation $x^{2} \cdot 2^{- x} = 1$ ?

The equation doesn't have a solution.

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The equation has

1

positive and

2

negative solutions.

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The equation has

2

positive and

1

negative solutions.

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The equation has all positive solutions.

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Solution

The correct option is C The equation has $2$ positive and $1$ negative solutions.
$x^{2} 2^{- x} = 1 \Rightarrow x^{2} = 2^{x}$
Assuming $f (x) = x^{2}; g (x) = 2^{x}$

Clearly, the equation has $1$ negative and $2$ positive solution.

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