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Mathematics
Problem
If for
z
=
α
+
i
β
z = \alpha + i\beta
z
=
α
+
i
β
,
∣
z
+
2
∣
=
z
+
4
(
1
+
i
)
|z + 2| = z + 4(1 + i)
∣
z
+
2∣
=
z
+
4
(
1
+
i
)
, then
α
+
β
\alpha + \beta
α
+
β
and
α
β
\alpha\beta
α
β
are the roots of the equation [April 8, 2023 (I)] (a)
x
2
+
7
x
+
12
=
0
x^2 + 7x + 12 = 0
x
2
+
7
x
+
12
=
0
(b)
x
2
+
3
x
−
4
=
0
x^2 + 3x - 4 = 0
x
2
+
3
x
−
4
=
0
(c)
x
2
+
2
x
−
3
=
0
x^2 + 2x - 3 = 0
x
2
+
2
x
−
3
=
0
(d)
x
2
+
x
−
12
=
0
x^2 + x - 12 = 0
x
2
+
x
−
12
=
0
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