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7
Polynomials with all roots <1
Polynomials with all roots <1
Source: Swiss TST 2023 P7
September 8, 2023
algebra
Problem Statement
Find all monic polynomials
P
(
x
)
=
x
2023
+
a
2022
x
2022
+
…
+
a
1
x
+
a
0
P(x)=x^{2023}+a_{2022}x^{2022}+\ldots+a_1x+a_0
P
(
x
)
=
x
2023
+
a
2022
x
2022
+
…
+
a
1
x
+
a
0
with real coefficients such that
a
2022
=
0
a_{2022}=0
a
2022
=
0
,
P
(
1
)
=
1
P(1)=1
P
(
1
)
=
1
and all roots of
P
P
P
are real and less than
1
1
1
.
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