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IMC
2003 IMC
6
polynomial
polynomial
Source: IMC-2003
May 5, 2004
algebra
polynomial
real analysis
real analysis unsolved
Problem Statement
Let
p
=
∑
k
=
0
n
a
k
X
k
∈
R
[
X
]
p=\sum\limits_{k=0}^n a_kX^k\in R[X]
p
=
k
=
0
∑
n
a
k
X
k
∈
R
[
X
]
a polynomial such that all his roots lie in the half plane
{
z
∈
C
∣
R
e
(
z
)
<
0
}
.
\{z\in C| Re(z)<0 \}.
{
z
∈
C
∣
R
e
(
z
)
<
0
}
.
Prove that
a
k
a
k
+
3
<
a
k
+
1
a
k
+
2
,
a_ka_{k+3}<a_{k+1}a_{k+2},
a
k
a
k
+
3
<
a
k
+
1
a
k
+
2
,
for every k=0,1,2...,n-3.
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