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Problem
Problem
If
a
∈
R
a \in \mathbb{R}
a
∈
R
and the equation
−
3
(
x
−
[
x
]
)
2
+
2
(
x
−
[
x
]
)
+
a
2
=
0
-3(x - [x])^2 + 2(x - [x]) + a^2 = 0
−
3
(
x
−
[
x
]
)
2
+
2
(
x
−
[
x
])
+
a
2
=
0
(where
[
⋅
]
[ \cdot ]
[
⋅
]
denotes the greatest integer function) has no integral solution, then all possible values of
a
a
a
lie in the interval a.
(
−
2
,
−
1
)
(-2, -1)
(
−
2
,
−
1
)
b.
(
−
∞
,
−
2
)
∪
(
2
,
∞
)
(-\infty, -2) \cup (2, \infty)
(
−
∞
,
−
2
)
∪
(
2
,
∞
)
c.
(
−
1
,
0
)
∪
(
0
,
1
)
(-1, 0) \cup (0, 1)
(
−
1
,
0
)
∪
(
0
,
1
)
d.
(
1
,
2
)
(1, 2)
(
1
,
2
)
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