Let f(x)=2 x^{2}-x-1 and S ={n in Z :|f(n)| l | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$f ( x )=2 x ^{2}- x -1$

$| f ( x )| \leq 800$

$2 n ^{2}- n -801 \leq 0$

$n^{2}-\frac{1}{2} n-\frac{801}{2} \leq 0$

$\left(n-\fr

Vedclass · Accepted Answer

$10620$

Vedclass · Answer

$f ( x )=2 x ^{2}- x -1$

$| f ( x )| \leq 800$

$2 n ^{2}- n -801 \leq 0$

$n^{2}-\frac{1}{2} n-\frac{801}{2} \leq 0$

$\left(n-\frac{1}{4}ight)^{2}-\frac{801}{2}-\frac{1}{16} \leq 0$

$\left(n-\frac{1}{4}ight)^{2}-\frac{6409}{16} \leq 0$

$\left(n-\frac{1}{4}-\frac{\sqrt{6409}}{4}ight)\left(n-\frac{1}{4}+\frac{\sqrt{6409}}{16}ight) \leq 0$

$\frac{1-\sqrt{6409}}{4} \leq n \leq \frac{1+\sqrt{6409}}{4}$

$n=\{-19,-18-17, \ldots \ldots 0,1,2, \ldots \ldots, 20\}$

$\sum_{n \in s} f(x)=\sum\left(2 x^{2}-x-1ight)$

$=2\left[19^{2}+18^{2}+\ldots . .+1^{2}+1^{2}+2^{2}+\ldots .+19^{2}+20^{2}ight]$

$=4\left[1^{2}+2^{2}+\ldots . .+19^{2}ight]+2\left[20^{2}ight]-20-40$

$=\frac{4 	imes 19 	imes 20 	imes(2 	imes 19+1)}{6}+2 	imes 400-60$

$=\frac{4 	imes 19 	imes 20 	imes 39}{6}+800-60-9880+800-60$

$=10620$

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 . . . . .

Similar Questions

Let $R =\{ a , b , c , d , e \}$ and $S =\{1,2,3,4\}$. Total number of onto function $f: R \rightarrow S$ such that $f(a) \neq$ 1 , is equal to $.............$.

Domain of $f (x)$ = $\sqrt {{{\log }_2}\left( {\frac{{10x - 4}}{{4 - {x^2}}}} \right) - 1} $ , is

Which of the following function is surjective but not injective

The function $f\left( x \right) = \left| {\sin \,4x} \right| + \left| {\cos \,2x} \right|$, is a periodic function with period

Let $S=\{1,2,3,4,5,6,7\} .$ Then the number of possible functions $f: S \rightarrow S$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in S$ and $m . n \in S$ is equal to $......$