1  # simple liear case
1 1
2  # quadratic with real roots
1 -5 6
2  # quadratic with complex roots
1 -5 7
2  # quadratic with zero linear coeff
1 0 1
2  # quadratic with equal roots
1 -2 1
3  # cubic with real roots
1 -4 1 6
3  # cubic with pair of complex roots
1 -4 2 7
3  # cubic with equal roots
1 -3 3 -1
3  # cubic with non-unity leading coefficient
24 -14 -1 -1
4  # quartic with real roots
1 -16 91 -216 180
4  # quartic with redundancy
1 1 0 0 0
20 # high order but ok
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
26 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
