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Mathematics
Mathematics
Problem
Let
z
1
z_1
z
1
and
z
2
z_2
z
2
be roots of the equation
z
2
+
p
z
+
q
=
0
z^2 + pz + q = 0
z
2
+
p
z
+
q
=
0
, where the coefficients
p
p
p
and
q
q
q
may be complex numbers. Let
A
A
A
and
B
B
B
represent
z
1
z_1
z
1
and
z
2
z_2
z
2
in the complex plane. If
△
A
O
B
=
η
≠
0
\triangle AOB = \eta \neq 0
△
A
O
B
=
η
=
0
and
O
A
=
O
B
OA = OB
O
A
=
O
B
, where
O
O
O
is the origin, prove that
p
2
=
4
q
cos
2
(
α
/
2
)
p^2 = 4q \cos^2(\alpha/2)
p
2
=
4
q
cos
2
(
α
/2
)
.
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