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RELATIONS AND FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
MCQ
Choose the correct answers: 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.
$x \in[2,3]$
  1. $x \in[2,3]$
Solution:
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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