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If [x]^(2)-5[x]+6=0, where [*] donate th...

If `[x]^(2)-5[x]+6=0`, where `[*]` donate the greatest integer function, then

A

`x in[3,4]`

B

`x in (2,3]`

C

`x in [2,4)`

D

`x in [2,4]`

Text Solution

Verified by Experts

The correct Answer is:
C
We have `[x]^(2)-5[x]+6=0`
`rArr [x]^(2)-3[x]-2[x]+6=0`
`rArr [x]([x]-3)-2([x]-3)=0`
`rArr([x)-3)([x]-2)=0`
`rArr [x]=2,3]`
`:. "x" in[2,3]`
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