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Austrian-Polish
1986 Austrian-Polish Competition
2
a_1P(1) > 2n^2a_o, monic polynomial
a_1P(1) > 2n^2a_o, monic polynomial
Source: Austrian Polish 1986 APMC
April 30, 2020
algebra
polynomial
monic
Problem Statement
The monic polynomial
P
(
x
)
=
x
n
+
a
n
−
1
x
n
−
1
+
.
.
.
+
a
0
P(x) = x^n + a_{n-1}x^{n-1} +...+ a_0
P
(
x
)
=
x
n
+
a
n
−
1
x
n
−
1
+
...
+
a
0
of degree
n
>
1
n > 1
n
>
1
has
n
n
n
distinct negative roots. Prove that
a
1
P
(
1
)
>
2
n
2
a
o
a_1P(1) > 2n^2a_o
a
1
P
(
1
)
>
2
n
2
a
o
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