restart:

N:=12: p:=Vector(N): a:=Vector(N-2):f:=(x)->x^4+5*x^3-9*x^2-85*x-136;

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCwqJDkkIiIlIiIiKiRGLiIiJCIiJiokRi4iIiMhIipGLiEjJikhJE8iRjBGJUYlRiU=

solve( f(x),x);

NiYqJCIjPCMiIiIiIiMsJEYjISIiLCYjISImRidGJiomXiNGJUYmIiIoRiVGJiwmRitGJiomXiMjRilGJ0YmRi9GJUYm

p0:=0: p1:=1: p2:= 1.5: p[1]:=p0: p[2]:=p1: p[3]:=p2:for i from 4 by 1 while (i<=N) do DD:=(p0-p2)*(p1-p2)*(p0-p1); c:= f(p2); b:= ( (p0-p2)^2*(f(p1)-f(p2)) - (p1-p2)^2*(f(p0)-f(p2))) / DD; a:= ( (p1-p2)*(f(p0)-f(p2)) - (p0-p2)*(f(p1)-f(p2)) ) / DD; p0:=p1; p1:=p2; p2:=evalf( p2-2*c/(b+sign(Re(b))*sqrt(b*b-4*a*c)) ); p[i]:=p2: end do:for i from 1 by 1 while (i<=N-2) do a[i]:=p[i] - (p[i+1]-p[i])^2 / (p[i+2]-2*p[i+1]+p[i]); printf(" (%2.ld ) ", i); printf("%13.8Zf ",p[i] ) ; printf("%13.8Zf\n",a[i] ); end do:

( 1 ) 0.00000000 +0.00000000I 2.00000000 +0.00000000I ( 2 ) 1.00000000 +0.00000000I 1.07636176 +0.00000000I ( 3 ) 1.50000000 +0.00000000I -2.11604382 +0.00000000I ( 4 ) -1.27389019 +0.00000000I -1.13239672 +0.33972304I ( 5 ) -1.91991159 +0.00000000I -2.55822078 +1.29717560I ( 6 ) -3.00195504 +1.04688035I -2.56504054 +1.25778914I ( 7 ) -2.65508011 +1.44833369I -2.49814415 +1.31879612I ( 8 ) -2.48194837 +1.29621367I -2.50001354 +1.32288692I ( 9 ) -2.49949378 +1.32234313I -2.50000000 +1.32287566I (10 ) -2.49999945 +1.32287642I -2.50000000 +1.32287566I

evalf( -5/2+1/2*I*7^(1/2) , 9);

NiNeJCQhKisrK10jISIpJCIqbXZHSyJGJg==