Question

The real roots of
$|x{|}^3-3x^2+3|x|-2=0$ are

• A. $0,2$
• B. $\pm 1$
• C. $\pm 2$
• D. $1,2$

Answer 1

Answer: (C)

$|x{|}^3-3|x^2+3x|-2$ = 0 [Clearly $|x|=2$ satisfies it]
$\Rightarrow (|x|-2)(|x{|}^2-|x|+1)=0$
$\Rightarrow |x|=2$ or $|x{|}^2-|x|+1=0$
$\Rightarrow |x|=2[\because |x{|}^2-|x|+1=0]$ has no real roots;
Disc = 1 - 4 = -ve]
$\Rightarrow x=\pm 2$