Q62 / 180 · KCET 2024 · Mathematics
If $[x]^2-5[x]+6=0$, where $[x]$ denotes the greatest integer function, then
- A$x \in[3,4]$
- Correct answerB$x \in[2,4)$
- C$x \in[2,3]$
- D$x \in(2,3]$
Solution
$[x]^2-5[x]+6=0$
$\Rightarrow \quad[x]^2-3[x]-2[x]+6=0$
$\Rightarrow \quad[x]([x]-3)-2([x]-3)=0$
$\Rightarrow \quad([x]-3)([x]-2)=0$
$\Rightarrow \quad[x]=2$ or 3
$[x]=2$ or $[x]=3$
$x=[2,3)$ or $x=[3,4)$
Hence, $x \in[2,4)$.
Hence, the correct answer is option: 'B'.