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Mathematics
Mathematics
Problem
Let
α
\alpha
α
and
β
\beta
β
be real and
z
z
z
be a complex number. If
z
2
+
α
z
+
β
=
0
z^2 + \alpha z + \beta = 0
z
2
+
α
z
+
β
=
0
has two distinct roots on the line
Re
(
z
)
=
1
\text{Re}(z) = 1
Re
(
z
)
=
1
, then it is necessary that a.
β
∈
(
−
1
,
0
)
\beta \in (-1, 0)
β
∈
(
−
1
,
0
)
b.
∣
β
∣
=
1
|\beta| = 1
∣
β
∣
=
1
c.
β
∈
(
1
,
∞
)
\beta \in (1, \infty)
β
∈
(
1
,
∞
)
d.
β
∈
(
0
,
1
)
\beta \in (0, 1)
β
∈
(
0
,
1
)
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