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1995 IMC
9
9
Part of
1995 IMC
Problems
(1)
IMC 1995 Problem 9
Source: IMC 1995
2/19/2021
Let all roots of an
n
n
n
-th degree polynomial
P
(
z
)
P(z)
P
(
z
)
with complex coefficients lie on the unit circle in the complex plane. Prove that all roots of the polynomial
2
z
P
′
(
z
)
−
n
P
(
z
)
2zP'(z)-nP(z)
2
z
P
′
(
z
)
−
n
P
(
z
)
lie on the same circle.
algebra
polynomial
complex analysis