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Question 220015
JEE Mathematics · Hard

Quadratic Equations and Inequalities: Integer roots MCQ

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Integer rootsHardQuestion 220015

Question

The number of integer values of k for which x² − 2(k−1)x + 4 > 0 for all real x is:
  1. A
    1
  2. B
    2
  3. C
    3
    Correct
  4. D
    Infinite

Correct answer

3

Explanation

A monic quadratic is positive for all real x when its discriminant is negative. Here 4(k−1)2−16<04(k-1)^2-16<0, so −1<k<3-1<k<3. The integer values are 0, 1, and 2: 3 values.

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