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Question 220032
JEE Mathematics · Hard

Quadratic Equations and Inequalities: Integer solutions MCQ

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Integer solutionsHardQuestion 220032

Question

The number of integers satisfying x² − 5|x| + 6 ≤ 0 is:
  1. A
    4
    Correct
  2. B
    6
  3. C
    8
  4. D
    2

Correct answer

4

Explanation

|x|² − 5|x| + 6 ≤ 0 → (|x|−2)(|x|−3) ≤ 0 → 2 ≤ |x| ≤ 3. So x ∈ [−3, −2] ∪ [2, 3]. Integer solutions: −3, −2, 2, 3 → 4 integers.

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