Question

If $\left[x^2\right]-5\left[x\right]+6=0,$ where $[\cdot ]$ denotes the greatest in integer function, then

• A. $x\in [3,4]$
• B. $x\in [2,4)$
• C. $x\in (2,3]$
• D. $x\in [2,3]$

Answer 1

The correct option is B $x\in [2,4)$

Given:$[x{]}^2-5[x]+6=0$

$\Rightarrow \left(\right[x]-2)\left(\right[x]-3)=0$

If $\left[x\right]=2$

$2\le x<3$

And if $\left[x\right]=3$

$3\le x<4$

Therefore, $x\in [2,4)$

Option (D) is correct.