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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Functions

NDA 2024 · Mathematics · Functions

If f(x)=[x]^2-30[x]+221=0 , where [x] is the greatest integer...

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

Options

  1. A1313
  2. B1717
  3. C2727
  4. D3030

Correct answer

D. 3030

Step-by-step solution

We are given. f(x)=[x]2−30[x]+221=0[x]=30±900−8842=30±42[x]=17 or 13\begin{aligned} & f(x)=[x]^2-30[x]+221=0 \\ & {[x]=\frac{30 \pm \sqrt{900-884}}{2}=\frac{30 \pm 4}{2}} \\ & {[x]=17 \text{ or } 13} \end{aligned} Integral value of x and 17 and 13. ∴\therefore Sum of integral solution of f(x)=30f(x)=30.
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