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GATE 2014 EE (EE2) – Question 8

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

For real x with $|x^2-2x+3|=11$, possible values of $|-x^3+x^2-x|$ include ______.

  1. 2, 4
  2. 2, 14
  3. 4, 52
  4. 14, 52

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Correct answer: (D) 14, 52

Explanation

The quadratic x²−2x+3=(x−1)²+2 is positive, so the given absolute equation yields x²−2x−8=0, with x=4 or−2. Substitution in |−x³+x²−x| gives52 and14 respectively. Hence **14,52,D**.