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9
2009 Algebra #9 - Minimum Value of Expression of Roots
2009 Algebra #9 - Minimum Value of Expression of Roots
Source:
January 2, 2012
Problem Statement
Let
f
(
x
)
=
x
4
+
14
x
3
+
52
x
2
+
56
x
+
16.
f(x) =x^4+14x^3+52x^2+56x+16.
f
(
x
)
=
x
4
+
14
x
3
+
52
x
2
+
56
x
+
16.
Let
z
1
,
z
2
,
z
3
,
z
4
z_1, z_2, z_3, z_4
z
1
,
z
2
,
z
3
,
z
4
be the four roots of
f
f
f
. Find the smallest possible value of
∣
z
a
z
b
+
z
c
z
d
∣
|z_az_b+z_cz_d|
∣
z
a
z
b
+
z
c
z
d
∣
where
{
a
,
b
,
c
,
d
}
=
{
1
,
2
,
3
,
4
}
\{a,b,c,d\}=\{1,2,3,4\}
{
a
,
b
,
c
,
d
}
=
{
1
,
2
,
3
,
4
}
.
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