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JEE Main202125 Feb 2021Morning ShiftMathematicsQuadratic EquationActual

The integer k , for which the inequality x 2 - 2 3 k - 1 x + 8 k 2 - 7 > 0 is valid for every x in R is:

Options

  1. A4
  2. B2
  3. C3
  4. D0

Correct answer

C. 3

Step-by-step solution

x 2 - 2 3 k - 1 x + 8 k 2 - 7 > 0 Now, D < 0 ⇒   4 3 k - 1 2 - 4 × 1 × 8 k 2 - 7 < 0 ⇒   9 k 2 - 6 k + 1 - 8 k 2 + 7 < 0 ⇒   k 2 - 6 k + 8 < 0 ⇒   k - 4 k - 2 < 0 ⇒   k ∈ 2 , 4 ⇒ k = 3

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