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Question 220023
JEE Mathematics · Hard

Quadratic Equations and Inequalities: Condition for real roots MCQ

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Condition for real rootsHardQuestion 220023

Question

For the equation x² − 2ax + a + 6 = 0 to have two real roots lying in (1, 4), the range of a is:
  1. A
    2 ≤ a ≤ 10
  2. B
    a ≥ 2
  3. C
    1 < a < 4
  4. D
    10/3 ≤ a ≤ 7
    Correct

Correct answer

10/3 ≤ a ≤ 7

Explanation

Need: D ≥ 0: 4a² − 4(a+6) ≥ 0 → a² − a − 6 ≥ 0 → a ≤ −2 or a ≥ 3. f(1) > 0: 1−2a+a+6=7−a>0→a<7. f(4)>0: 16−8a+a+6=22−7a>0→a<22/7. Vertex in (1,4): 1

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