The number of real solutions of the equation $- x^{2} + x - 1 = {sin}^{4} x$ is

1

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2

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0

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4

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Solution

The correct option is C $0$
$\begin{matrix} - [x^{2} - x + 1] = {sin}^{4} x - [{(x - \frac{1}{2})}^{2} + \frac{3}{4}] = {sin}^{4} x - \frac{3}{4} - {(x - \frac{1}{2})}^{2} = {sin}^{4} x sin c e L H S < 0 a n d R H S \geq 0 \Rightarrow G i v e n e q u a t i o n h a s n o s o l u t i o n . H e n c e, o p t i o n C i s c o r r e c t a n s w e r . \end{matrix}$

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