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

1.	If [x]2 – 5 [x] + 6 = 0, where [ . ] denote the greatest integer function, thenA. x ∈ [3, 4]B. x ∈ (2, 3]C. x ∈ [2, 3]D. x ∈ [2, 4)
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).

If [x]2 – 5 [x] + 6 = 0, where [ . ] denote the greatest integer function, thenA. x ∈ [3, 4]B. x ∈ (2, 3]C. x ∈ [2, 3]D. x ∈ [2, 4)

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).