JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f(x)=2 x^{2}-x-1\) and \(S =\{n \in Z :|f(n)| \leq 800\}\) . Then value of \(\sum_{n \in S} f(n)\) is . . . . .
- A \(10620\)
- B \(10630\)
- C \(10640\)
- D \(10650\)
Answer & Solution
Correct Answer
(A) \(10620\)
Step-by-step Solution
Detailed explanation
\(f ( x )=2 x ^{2}- x -1\) \(| f ( x )| \leq 800\) \(2 n ^{2}- n -801 \leq 0\) \(n^{2}-\frac{1}{2} n-\frac{801}{2} \leq 0\) \(\left(n-\frac{1}{4}\right)^{2}-\frac{801}{2}-\frac{1}{16} \leq 0\) \(\left(n-\frac{1}{4}\right)^{2}-\frac{6409}{16} \leq 0\)…
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