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f f(x) = 9x - 8√x such that g(x) = f(x) - 1, then which one of the following is correct?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. g(x) = 0 has no real roots 
  2. g(x) = 0 has only one real root which is an integer 
  3. g(x) = 0 has two real roots which are integers 
  4. g(x) = 0 has only one real root which is not an integer 

Answer (Detailed Solution Below)

Option 2 : g(x) = 0 has only one real root which is an integer 
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Detailed Solution

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Explanation:

Given:

f(x) = 9x - 8√x 

g(x) = f(x) - 1

Let x = t2

⇒ g(t2 ) = 9t2 – 8t – 1 = 0

⇒ t = \(\frac{8± 10}{18} = 1, \frac{-1}{9}\)

⇒ x = 1 , 1/81

 g(x) = 0 has only one real root which is an integer.

∴ Option (b) is correct.

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