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For p > 2 and x ∈ R , if the number of natural numbers in the range of f x = x 2 + 2 x + p x 2 + 2 x + 2 is 3 , then the value of p is equal to

Options

  1. A3
  2. B4
  3. C5
  4. D6

Correct answer

C. 5

Step-by-step solution

Here, f x = 1 + p - 2 x + 1 2 + 1 ∈ 1 , p - 1 If there are 3 natural numbers in the range ⇒ p - 1 = 4 ⇒ p = 5

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