find roots.m running
some examples have roots on unit circle
x^2+1=0
p2 =
     1     0     1
r2 =
   0.0000 + 1.0000i
   0.0000 - 1.0000i

x^3+1=0
p3 =
     1     0     0     1
r3 =
  -1.0000 + 0.0000i
   0.5000 + 0.8660i
   0.5000 - 0.8660i

x^4+1=0
p4 =
     1     0     0     0     1
r4 =
  -0.7071 + 0.7071i
  -0.7071 - 0.7071i
   0.7071 + 0.7071i
   0.7071 - 0.7071i

x^5+1=0
p5 =
     1     0     0     0     0     1
r5 =
  -1.0000 + 0.0000i
  -0.3090 + 0.9511i
  -0.3090 - 0.9511i
   0.8090 + 0.5878i
   0.8090 - 0.5878i

x^6+1=0
p6 =
     1     0     0     0     0     0     1
r6 =
  -0.8660 + 0.5000i
  -0.8660 - 0.5000i
   0.0000 + 1.0000i
   0.0000 - 1.0000i
   0.8660 + 0.5000i
   0.8660 - 0.5000i

5 x^2 -6 x +5 =0
pq =
     5    -6     5
rq =
   0.6000 + 0.8000i
   0.6000 - 0.8000i

x^2 -x + 3  not unit
pd =
     1    -1     3
rd =
   0.5000 + 1.6583i
   0.5000 - 1.6583i

x^2 - 1  real
pa =
     1     0    -1
ra =
    -1
     1

x^2 -3 x + 2  real
pr =
     1    -3     2
rr =
     2
     1

x^4 -10 x^3 +35 x^2 -50 x + 24  real
(x-1)*(x-2)*(x-3)*(x-4)
ps =
     1   -10    35   -50    24
rs =
    4.0000
    3.0000
    2.0000
    1.0000

x^2 -50 x + 0.5  big, small
pb =
    1.0000  -50.0100    0.5000
rb =
   50.0000
    0.0100

quit