Question

# The set of values of $$x$$ for which the inequality $$\displaystyle \left [ x \right ]^{2}-5[x]+6\leq 0$$ (where $$[.]$$ denote the greatest integral function) holds good are

A
2[x]<3
B
2x<4
C
2[x]3
D
(b) and (c) both

Solution

## The correct option is D $$(b)$$ and $$(c)$$ bothWe have,  $$\displaystyle \left [ x \right ]^{2}-5[x]+6\leq 0$$Let $$[x] =y$$$$\Rightarrow y^2-5y+6\le 0$$$$\Rightarrow (y-2)(y-3) \le 0$$$$\Rightarrow y\in [2,3]$$$$\Rightarrow [x]\in [2,3]$$$$\therefore x\in [2,4)$$Mathematics

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