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AIME Problems
1995 AIME Problems
5
5
Part of
1995 AIME Problems
Problems
(1)
Complex Roots
Source:
12/22/2005
For certain real values of
a
,
b
,
c
,
a, b, c,
a
,
b
,
c
,
and
d
,
d,
d
,
the equation
x
4
+
a
x
3
+
b
x
2
+
c
x
+
d
=
0
x^4+ax^3+bx^2+cx+d=0
x
4
+
a
x
3
+
b
x
2
+
c
x
+
d
=
0
has four non-real roots. The product of two of these roots is
13
+
i
13+i
13
+
i
and the sum of the other two roots is
3
+
4
i
,
3+4i,
3
+
4
i
,
where
i
=
−
1
.
i=\sqrt{-1}.
i
=
−
1
.
Find
b
.
b.
b
.
algebra
polynomial
Vieta
complex numbers