Question

If $[x{]}^2-5[x]+6=0$, where [.] denotes the greatest integer function, then

• A. $xϵ[3,4]$
• B. $xϵ(2,3]$
• C. $xϵ[2,3]$
• D. $xϵ[2,4]$

Answer 1

The correct option is C

$xϵ[2,3]$

We have, $[x{]}^2-5[x]+6=0$ $\Rightarrow [x{]}^2-3[x]-2[x]+6=0\Rightarrow [x\left]\right(\left[x\right]-3)-2(\left[x\right]-3)=0\Rightarrow (\left[x\right]-3\left)\right(\left[x\right]-2)=0\Rightarrow [x]=2,3\therefore xϵ[2,3]$