Answer :

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


To find: range of x


Explanation: we have


[x]2 – 5 [x] + 6 = 0


We will split the middle term, we get


[x]2 – 3 [x] -2[x] + 6 = 0


[x]([x]–3)-2([x]-3) = 0


([x]-3)([x]-2) = 0


[x]-3 = 0 or [x]-2 = 0


[x] = 3 or [x] = 2


[x] = 2, 3


For [x] = 2, x [2,3)


For [x] = 3, x [3,4)


[x] [2,3) [3,4)


So, x [2,4]


Hence the correct answer is option (C).

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