The polynomial has two extremely close real roots (20 common digits)
plus a complex pair with extremely small imaginary part.
The remaining roots are well separated, one of them is real: .
The condition number of the above clustered
roots is greater than
More difficult situations can be obtained with larger values of the
parameter c.
For we have roots with 70
common digits and nonzero imaginary part of modulus less than
.
For we have roots with about 247 common digits and nonzero
imaginary part
of modulus less than
.