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

Given $|x{|}^2-3|x|+2=0$

Here we consider two cases viz.x < 0 and x > 0

Case 1: x < 0 This gives $x^2+3x+2=0$

⇒ $(x+2)(x+1)=0$ ⇒ $x=-2,-1$

Also $x=-1,-2$ satisfy $x<0,$ so $x=-1,-2$ is solution in this case

Case 2: x > 0. This gives $x^2-3x+2=0$

⇒ (x-2)(x-1) = 0 ⇒ x =2,1. so, x=2,1 is solution in this case. Hence the number5 of solutions are four i.e. x = -1, -2, 1, 2

Aliter : $|x{|}^2-3|x|+2=0$

⇒ (|x|-1)(|x|-2)=0

⇒ |x| = 1 and |x| = 2 ⇒ x = ±1, x = ±2.