If $f(x)=[x]^{2}-5[x]+6=0$, where $[x]$ denotes greatest integer function then $x \in$
If $f(x)=[x]^{2}-5[x]+6=0$, where $[x]$ denotes greatest integer function
then $x \in$
$(2,4]$
$[2,4]$
$[2,4)$
$(2,4)$
Solution
We have, $[x]^{2}-5[x]+6=0$
$\therefore([x]-3)([x]-2)=0 \Rightarrow[x]=2,3$
For $[x]=2, x \in[2,3)$ and for $[x]=3, x \in[3,4)$
$\therefore \quad x \in[2,4)$