Quadratic???

Algebra Level 3

The number of real roots of the equation

x 2 − 3 ∣ x ∣ + 2 = 0 { x }^{ 2 }-3|x|+2=0 is

4 2 no real roots 1

Krishna Ramesh by Krishna Ramesh , 22, India

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3 solutions

Max Yuen
May 6, 2019

The equation factors into ( ∣ x ∣ − 1 ) ( ∣ x ∣ − 2 ) = 0 (|x|-1)(|x|-2)=0

The solutions can be obtained by inspection:

x = 1 , − 1 , 2 , − 2 x=1,-1,2,-2

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Derek Zhu
Jun 17, 2015

Because the absolute value of x can mean that that number could actually be positive or negative. The equation x^2-3x+2=0 has 2 solutions and the equation x^2+3x+2=0 also has 2 solutions. There are a total of 4 solutions (2+2).

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Saurav Pal
Feb 26, 2015

x 2 − 3 ∣ x ∣ + 2 = 0 x^{2}-3|x|+2=0 will be divided into two sub-cases. CASE 1. x 2 − 3 x + 2 = 0 x^{2}-3x+2=0 which will give x = 1 , 2 x=1,2 .
CASE 2. x 2 + 3 x + 2 = 0 x^{2}+3x+2=0 which will give x = − 1 , − 2 x=-1,-2 .
Hence there are total 4 \boxed {4} solutions.

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