Question

The set of values of $x$ for which the inequality ${\left[x\right]}^2-8\left[x\right]+15\le 0$ (where $\left[x\right]$ denote the greatest integer function) hold if

• A. $3<\left[x\right]<5$
• B. $3\le x<6$
• C. $3\le \left[x\right]\le 5$
• D. (b) and (c) both

Answer 1

The correct option is D (b) and (c) both

${\left[x\right]}^2-8\left[x\right]+15\le 0$
$\Rightarrow (\left[x\right]-3)(\left[x\right]-5)\le 0\Rightarrow 3\le \left[x\right]\le 5$
$\Rightarrow 3\le x<6$