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JEE Main 2019 · Mathematics · Quadratic Equations · medium

The number of integer values of k in the interval [-10,10] for which x^2+kx+4=0 has real roots is

Single correct option

The number of integer values of kk in the interval [−10,10][-10,10] for which x2+kx+4=0x^2+kx+4=0 has real roots is
  1. A. 14
  2. B. 12
  3. C. 11
  4. D. 16
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Answer: (A) 14

Real roots need D=k2−16≥0D=k^2-16\ge0, i.e. ∣k∣≥4|k|\ge4. Integers −10≤k≤−4-10\le k\le-4 give 7 values and 4≤k≤104\le k\le10 give 7 values, so the total is 14 (the equality case ∣k∣=4|k|=4 must be included).
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