Question

The number of real solutions of the equation $|x{|}^2-3|x|+2=0$ are

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is D 4

Conventional Method :
Given $|x{|}^2-3|x|+2=0$
Here we consider two cases viz. $x<0$ and $x>0$
Case I : $x<0$. This gives $x^2+3x+2=0\Rightarrow (x+2)(x+1)=0\Rightarrow x=-2,-1$ Also $x=-1,-2$ satisfy $x<0$,, so $x=-1,-2$ are solutions in this case.
Case II: $x>0$. This gives $x^2-3x+2=0\Rightarrow (x-2)(x-1)=0\Rightarrow x=2,1sox=2,1$ are solutions in this case. Hence, the number of solutions are four $i.e.,x=-1,1,2,-2$
Alternate Method : $|x{|}^2-3|x|+2=0(|x|-1)(|x|-2)=0|x|=1$ and $|x|=2x=\pm 1,x=\pm 2.$