Question

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

• A. $-1$
• B. $-2$
• C. $1$
• D. $2$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $-1$
B $-2$
C $1$
D $2$

We know that
$\text{sgn}x=\{\begin{array}{c}1x>0\\ 0x=0\\ -1x<0\end{array}$

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

$\text{(ii)}x=0$
Then $2=0$
Not possible.

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