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If one root is greater than 2 and the other root is less than 2 for the equation x 2 - k + 1 x + k 2 + k - 8 = 0 , then the value of k lies between

Options

  1. A- 2,2
  2. B- 2,4
  3. C- 2,0
  4. D- 2,3

Correct answer

D. - 2,3

Step-by-step solution

Opening upward parabola, 2 lies between the roots. ⇒ f 2 < 0 4 - k + 1 2 + k 2 + k - 8 < 0 k 2 + k - 8 - 2 k - 2 + 4 < 0 k 2 - k - 6 < 0 k - 3 k + 2 < 0 ⇒ k ∈ - 2,3

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