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

.