Number of roots of the equation $x^{2} - 2 x - {log}_{2} | 1 - x | = 3$ is

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Solution

$x^{2} - 2 x - {log}_{2} | 1 - x | = 3$
$\Rightarrow x^{2} - 2 x - 3 = {log}_{2} | 1 - x |$
Draw the graph of $x^{2} - 2 x - 3$ and ${log}_{2} | 1 - x |$

From graph, there are $4$ points of intersection.

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