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Relations and Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsRelations and Functions1 Mark
MCQ
If $[x]^2 - 5[x] + 6 = 0,$ where $[.]$ denote the greatest integer function$,$ then.
  • A
    $x \in [3, 4]$
  • B
    $x \in (2, 3]$
  • ✓
    $x \in [2, 3]$
  • D
    $x \in [2, 4]$
✓

Answer

Correct option: C.
$x \in [2, 3]$
We have $[x]^2 - 5[x] + 6 = 0$
$\Rightarrow [x]^2 - 3[x] 2[x] + 6 = 0$
$\Rightarrow [x]([x] - 3) -2([x] - 3) = 0$
$\Rightarrow ([x] - 3)([x] - 2) = 0$
$\Rightarrow [x] = 2, 3$
So$, x \in [2, 3]$

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