lf f(x) = [x]2 - 30[x] + 221 = 0, where [x] is the greatest integer function, then what is the sum of all integer solutions? 

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 13
  2. 17
  3. 27
  4. 30

Answer (Detailed Solution Below)

Option 4 : 30
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Detailed Solution

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Explanation:

f(x) = [x]2 – 30[x] + 221 = 0 

⇒ [x] = \(\frac{30± \sqrt{900-884}}{2} = \frac{30±4}{2}\)

⇒ [x] = \(\frac{30+ 4}{2 }, \frac{30 -4 }{2}\)

⇒ [x] = 17 , 13

Thus, Sum of integral solution of f(x) = 30.

∴ Option (d) is correct

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