Jensen's Disks

degree of polynomial

3

4

5

6

complex

coefficients

seed

Jensen's theorem states that for any nonconstant polynomial

p(z)

with real coefficients, every nonreal root of

p'(z)

lies inside a disk determined by some pair of conjugate nonreal zeros of

p(z)

. Blue dots are roots of

p(z)

, orange dots are nonreal roots of

p'(z)

, and gray disks are real roots of

p'(z)

.