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1994 Moldova Team Selection Test
1
Find $\max\{P(-2),P(2)\}$
Find $\max\{P(-2),P(2)\}$
Source: Moldova TST 1994
August 8, 2023
algebra
polynomial
Problem Statement
Let
P
(
X
)
=
X
n
+
a
1
X
n
−
1
+
…
+
a
n
P(X)=X^n+a_1X^{n-1}+\ldots+a_n
P
(
X
)
=
X
n
+
a
1
X
n
−
1
+
…
+
a
n
be a plynomial with real roots
x
1
.
x
2
,
…
,
x
n
x_1. x_2,\ldots,x_n
x
1
.
x
2
,
…
,
x
n
. Denote
E
k
=
x
1
k
+
x
2
k
+
…
+
x
n
k
,
∀
k
∈
N
E_k=x_1^k+x_2^k+\ldots+x_n^k, \forall k\in\mathbb{N}
E
k
=
x
1
k
+
x
2
k
+
…
+
x
n
k
,
∀
k
∈
N
. There exists an
m
∈
N
m\in\mathbb{N}
m
∈
N
such that
E
m
=
E
m
+
1
=
E
m
+
2
=
1
E_m=E_{m+1}=E_{m+2}=1
E
m
=
E
m
+
1
=
E
m
+
2
=
1
. Find
max
{
P
(
−
2
)
,
P
(
2
)
}
\max\{P(-2),P(2)\}
max
{
P
(
−
2
)
,
P
(
2
)}
.
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