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added 94 characters in body
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97.100.97.109
97.100.97.109
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Python, 143143 134 133 bytes

deff=lambda f(a,b,c,d,R=[-1,1j,1]):
    for i in" "*99[R:R=[=[(z:=R[2])-(((a*z+b)*z+c)*z+d)/(z-R[0])/(z-R[1])]+R
  for i in" return[x"*99]and[x for x in R[:3]if x.imag==0.0]imag==0]

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This is the first solution that doesn't use a builtin, and it suffers greatly for it. Instead, I'm using the Durant-Kerner method to find all approximations, then filtering for whether they're complex.

-9 bytes from @Steffan for various small changes.

Python, 143 bytes

def f(a,b,c,d,R=[-1,1j,1]):
    for i in" "*99:R=[(z:=R[2])-(((a*z+b)*z+c)*z+d)/(z-R[0])/(z-R[1])]+R
     return[x for x in R[:3]if x.imag==0.0]

Attempt This Online!

This is the first solution that doesn't use a builtin, and it suffers greatly for it. Instead, I'm using the Durant-Kerner method to find all approximations, then filtering for whether they're complex.

Python, 143 134 133 bytes

f=lambda a,b,c,d,R=[-1,1j,1]:[R:=[(z:=R[2])-(((a*z+b)*z+c)*z+d)/(z-R[0])/(z-R[1])]+R for i in" "*99]and[x for x in R[:3]if x.imag==0]

Attempt This Online!

This is the first solution that doesn't use a builtin, and it suffers greatly for it. Instead, I'm using the Durant-Kerner method to find all approximations, then filtering for whether they're complex.

-9 bytes from @Steffan for various small changes.

Source Link
97.100.97.109
97.100.97.109
  • 7.1k
  • 12
  • 46

Python, 143 bytes

def f(a,b,c,d,R=[-1,1j,1]):
    for i in" "*99:R=[(z:=R[2])-(((a*z+b)*z+c)*z+d)/(z-R[0])/(z-R[1])]+R
    return[x for x in R[:3]if x.imag==0.0]

Attempt This Online!

This is the first solution that doesn't use a builtin, and it suffers greatly for it. Instead, I'm using the Durant-Kerner method to find all approximations, then filtering for whether they're complex.