IIT JEE 1982 Maths - MCQ Question 2

Algebra Level 2

The number of real solutions of the equation ∣ x ∣ 2 − 3 ∣ x ∣ + 2 = 0 |x|^2 - 3|x| + 2=0 is ______ . \text{\_\_\_\_\_\_}.

Notation: ∣ ⋅ ∣ | \cdot | denotes the absolute value function .

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Shubhamkar Ayare by Shubhamkar Ayare , 22, India

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1 solution

Tom Engelsman
Nov 29, 2016

The above equation factors into ( ∣ x ∣ − 1 ) ( ∣ x ∣ − 2 ) = 0 ⇒ ∣ x ∣ = 1 , 2 ⇒ x = ± 1 , ± 2. (|x| - 1)(|x| - 2) = 0 \Rightarrow |x| = 1, 2 \Rightarrow x = \pm1, \pm2. We have four solutions total (choice B).

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