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NDA 2016 Maths · Mathematics · Quadratic Equations · medium

The number of real solutions of the equation x^2-3|x|+2=0 is

Single correct option

The number of real solutions of the equation x2−3∣x∣+2=0x^2-3|x|+2=0 is
  1. A. 22
  2. B. 44
  3. C. 33
  4. D. 11
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Answer: (B) 44

Since x2=∣x∣2x^2=|x|^2, put t=∣x∣t=|x|: t2−3t+2=0t^2-3t+2=0 gives t=1t=1 or t=2t=2. Each positive value of ∣x∣|x| gives two real values of xx, namely ±1\pm1 and ±2\pm2, so there are 4 solutions. Solving as an ordinary quadratic and stopping at the two values of tt gives the trap answer 2.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake