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KCET2024MathematicsFunctions

If [x]^2-5[x]+6=0 , where [x] denotes the greatest integer function, then

Options

  1. Ax [3,4]
  2. Bx [2,4)
  3. Cx [2,3]
  4. Dx (2,3]

Correct answer

B. x [2,4)

Step-by-step solution

[x]^2-5[x]+6=0 [x]^2-3[x]-2[x]+6=0 [x]([x]-3)-2([x]-3)=0 ([x]-3)([x]-2)=0 [x]=2 or 3 [x]=2 or [x]=3x=[2,3) or x=[3,4) Hence, x [2,4) .

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