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Problems
Let
A
=
{
a
∈
R
∣
the equation
(
1
+
2
i
)
x
3
−
2
(
3
+
i
)
x
2
+
(
5
−
4
i
)
x
+
2
a
2
=
0
has at least one real root
}
A = \{a \in \mathbb{R} \mid \text{the equation } (1+2i)x^3 - 2(3+i)x^2 + (5-4i)x + 2a^2 = 0 \text{ has at least one real root}\}
A
=
{
a
∈
R
∣
the equation
(
1
+
2
i
)
x
3
−
2
(
3
+
i
)
x
2
+
(
5
−
4
i
)
x
+
2
a
2
=
0
has at least one real root
}
…
Mathematics
Problem
Let
A
=
{
a
∈
R
∣
the equation
(
1
+
2
i
)
x
3
−
2
(
3
+
i
)
x
2
+
(
5
−
4
i
)
x
+
2
a
2
=
0
has at least one real root
}
A = \{a \in \mathbb{R} \mid \text{the equation } (1+2i)x^3 - 2(3+i)x^2 + (5-4i)x + 2a^2 = 0 \text{ has at least one real root}\}
A
=
{
a
∈
R
∣
the equation
(
1
+
2
i
)
x
3
−
2
(
3
+
i
)
x
2
+
(
5
−
4
i
)
x
+
2
a
2
=
0
has at least one real root
}
. Find the value of
∑
a
∈
A
a
2
\sum_{a \in A} a^2
∑
a
∈
A
a
2
.
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