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Italy TST
1998 Italy TST
4
polynomials whose zeros are exactly a_1,a_2,...,a_n
polynomials whose zeros are exactly a_1,a_2,...,a_n
Source: Italy TST 1998 p4
February 16, 2020
algebra
polynomial
Problem Statement
Find all polynomials
P
(
x
)
=
x
n
+
a
1
x
n
−
1
+
.
.
.
+
a
n
P(x) = x^n +a_1x^{n-1} +...+a_n
P
(
x
)
=
x
n
+
a
1
x
n
−
1
+
...
+
a
n
whose zeros (with their multiplicities) are exactly
a
1
,
a
2
,
.
.
.
,
a
n
a_1,a_2,...,a_n
a
1
,
a
2
,
...
,
a
n
.
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