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Miklós Schweitzer
2019 Miklós Schweitzer
7
7
Part of
2019 Miklós Schweitzer
Problems
(1)
Roots of P' are in {z: |P(z)| = 1}
Source: Miklós Schweitzer 2019, Problem 7
12/27/2019
Given a polynomial
P
P
P
, assume that
L
=
{
z
∈
C
:
∣
P
(
z
)
∣
=
1
}
L = \{z \in \mathbb{C}: |P(z)| = 1\}
L
=
{
z
∈
C
:
∣
P
(
z
)
∣
=
1
}
is a Jordan curve. Show that the zeros of
P
′
P'
P
′
are in the interior of
L
L
L
.
algebra
college contests
Miklos Schweitzer
complex analysis