Q63 / 150 · MHT CET 2020 (14 Oct Shift 1) · Mathematics

If $f(x)=[x]^{2}-5[x]+6=0$, where $[x]$ denotes greatest integer function then $x \in$

  • A
    $(2,4]$
  • B
    $[2,4]$
  • Correct answer
    C
    $[2,4)$
  • D
    $(2,4)$

Solution

We have, $[x]^{2}-5[x]+6=0$ $\therefore([x]-3)([x]-2)=0 \Rightarrow[x]=2,3$ For $[x]=2, x \in[2,3)$ and for $[x]=3, x \in[3,4)$ $\therefore \quad x \in[2,4)$

Hence, the correct answer is option: 'C'.

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