The number of roots of the equation $| x - x^{2} - 2 | = | 2 x - 3 - x^{2} |$ is

0

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1

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2

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infinitely

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Solution

The correct option is A $1$
$| x - x^{2} - 2 | = | 2 x - 3 - x^{2} |$
$\Rightarrow x - x^{2} - 2 = \pm (2 x - 3 - x^{2})$
$\Rightarrow x - x^{2} - 2 = 2 x - 3 - x^{2} or x - x^{2} - 2 = - (2 x - 3 - x^{2})$
$\Rightarrow x = 1 or 2 x^{2} - 3 x + 5 = 0 \Rightarrow D = (- 3)^{2} - 4.2.5 - 31 < 0$
Hence, there is only one root of the given equation $x = 1$ .

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