Solve `x^2+3x+9=0`

Answer

B

Explanation

`:'x-[x]={x}` [fractional part of `x`]
For no integral solution `{x}!=0`
`:.a!=0`……….i
The given equation can be written as
`3{x}^(2)-2{x}-a^(2)=0`
`implies{x}=(2+sqrt((4+12a^(2)))/6=(1+sqrt((1+3a^(2)))/3[:'0lt{x}lt1]`
`implies0lt(1+sqrt((1+3a^(2)))/3lt1impliessqrt(1+3a^(2)))lt2`
`impliesa^(2)lt1=-1ltalt1` ..........ii
From Eqs i and ii we get
`a epsilon(-1,0)uu(0,1)`