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NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice

The number of natural numbers n for which the equation x - 8 x = n n - 10 has no real solution is equal to

Options

  1. A2
  2. B3
  3. C4
  4. D5

Correct answer

D. 5

Step-by-step solution

x 2 - 8 x - n n - 10 = 0 has no real solution. ⇒ 64 + 4 n n - 10 < 0 ⇒ n 2 - 10 n + 16 < 0 ⇒ n - 8 n - 2 < 0 ⇒ 2 < n < 8 ⇒ n = 3,4 , 5,6 , 7 ⇒ Number of values of n is 5

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