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WOLFRAM|DEMONSTRATIONS PROJECT

Zeros of a Perturbed Polynomial

​
n
1
2
3
4
5
6
7
8
9
a
Define the polynomials
P(z)=1+z+
2
z
+…+
n
z
and
P
a
(z)=1+z+
2
z
+…+(1+a)
n
z
,
a≥0
, the perturbed polynomial of
P(z)
.
The zeros of
P(z)
and
P
a
(z)
are shown by black and red points, respectively.
The zeros of
P(z)
lie on the unit circle and the zeros of
P
a
(z)
lie inside the unit circle when
a>0
.
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