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Real Valued Functions

If x2-3x sgn ...

Question

If $x^{2} - 3 x sgn (x) + 2 = 0,$ then the value(s) of $x$ is/are
(where $sgn (x)$ denotes the signum function)

- 1

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- 2

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1

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2

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Solution

The correct option is D $2$
We know that
$sgn x = ⎧ ⎨ ⎩ \begin{matrix} 1 x > 0 0 x = 0 - 1 x < 0 \end{matrix}$

$(i) x > 0$
Then $x^{2} - 3 x + 2 = 0$
$\Rightarrow (x - 1) (x - 2) = 0 \Rightarrow x = 1, 2$

$(ii) x = 0$
Then $2 = 0$
Not possible.

$(iii) x < 0$
Then $x^{2} + 3 x + 2 = 0$
$\Rightarrow (x + 1) (x + 2) = 0 \Rightarrow x = - 1, - 2$

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