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If a in R and the equation -3(x-[x])^2+2...

If `a in R` and the equation `-3(x-[x])^2+2(x-[x])+a^2=0` (where [x] denotes the greatest integer `le x`) has no integral solution, then all possible values of a lie in the interval: (1) (-2,-1) (2) `(oo,-2) uu (2,oo)` (3) `(-1,0) uu (0,1)` (4) (1,2)

A

`(-1,0) cup (0,1)`

B

`(1,2)`

C

`(-2,-1)`

D

`(-oo,-2)cup (2,oo)`

Text Solution

Verified by Experts

The correct Answer is:
A
`a^(2)=3t^(2)-2t, " where " t={x} in [0,1)`
` :. a^(2) =3t(t-2//3)`
Graph of `f(t)=3t(t-2//3)` is as shown in the following figure.

Clearly, from graph
`0 lt a^(2) lt 1`
`or a in (-1,0) cup (0,1) `
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