The number of real solutions of the equation:
$2^{x} = - 5 + x - 2 x^{2}$ is

0

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1

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2

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none of these

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Solution

The correct option is A $0$

$2^{x} = - 5 + x - 2 x^{2}$

$f (x) = - 5 + x - 2 x^{2}$

$d i s c r i m i n a n t = 1 - 4 \times 10 < 0$

Roots are imaginary and $f (x)$ is always negative

$2^{x} > 0$

So these two curves never intersect which means no solution

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