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  4. The set of value of x for which the inequality [x]2-5[x]+6 le 0 (where [·] denote the greatest integral function) hold good if

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Q. The set of value of x for which the inequality $[x]^{2}-5[x]+6 \le\,0$ (where $[·]$ denote the greatest integral function) hold good if

Complex Numbers and Quadratic Equations

Solution:

$[x]^{2}-5 [x]+6 \le \,0$
$\Rightarrow ([x]-2) ([x]-3) \le\, 0$
$\Rightarrow 2 \le [x] \, \le 3$
$\Rightarrow 2 \, \le \, [x] \le\,3$
$\Rightarrow 2 \,\le x \le \,4$