Question

Complete solution set of $2[x{]}^2-11[x]+12\le 0$ where $[.]$ represents greatest integer function, is

• A. $[3,5)$
• B. $[4,5)$
• C. $[2,5)$
• D. None of these

Answer 1

Answer: (C)

$[2,5)$

$2[x{]}^2-11[x]+12\le 0,$

$\Rightarrow 2[x{]}^2-11[x]+12\le 0,\Rightarrow (2\left[x\right]-3\left)\right(\left[x\right]-4)\le 0$

$\Rightarrow \left[x\right]=\{2,3,4\}\Rightarrow x\in [2,5)$