Question

If [x]² – 5 [x] + 6 = 0, where [ . ] denote the greatest integer function, then

(A) x ∈ [3, 4] 

(B) x ∈ (2, 3]

(C) x ∈ [2, 3] 

(D) x ∈ [2, 4)

Answer 1

Answer is (D)

We have [x]² – 5[x] + 6 = 0 => [(x – 3)([x] – 2) = 0

=> [x] = 2 , 3 .

For [x] = 2, x ∈ [2, 3)

For [x] = 3, x ∈ [3,4)

x ∈ [2, 3) u [3,4)

Or x ∈ [2,4)