Sum of all the roots of the equation $x^{2} - 2 x + | x - 1 | - 5 = 0$ is

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Solution

The correct option is A 2
Given equation can be written as $| x - 1 |^{2} + | x - 1 | - 6 = 0$
$(| x - 1 | - 2) (| x - 1 | + 3) = 0 ∴ | x - 1 | = 2 \Rightarrow x = 3, - 1 \Rightarrow 3 - 1 = 2$

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