i have the solution here is it:
this calculates only the real roots
they are Rx(0), Rx(1), Rx(2)
i am using this code in my AiEditor for Racer
my Site
here a pic of this
Function FindRootsPoly3(A3#,A2#,A1#,A0#) Local fc2#,gc2#,hc2#,Rc2#,Sc2#,Tc2#,Uc2#,ic2#,jc2#,kc2#,Lc2#,Mc2#,Nc2#,Pc2# fc2 =( (3*A1/A3) - ((A2^2)/(A3^2) ))/ 3 gc2=(( (2*A2^3)/(A3^3)) - (9*A2*A1/(A3^2)) + (27*A0/A3)) / 27 hc2 = ((gc2^2)/4) + ((fc2^3)/27) If hc2>0 Then Rc2 = -(gc2/2) + (Sqr(hc2)) If Rc2<0 Then Sc2 = -(Abs(Rc2)^0.333333) Else Sc2 = ((Rc2))^0.333333 EndIf Tc2 = -(gc2/2) -( Sqr(hc2)) If Tc2<0 Then Uc2 = -(Abs(Tc2)^0.333333) Else Uc2 = (Tc2)^0.333333 EndIf Rx(0) = (Sc2 + Uc2) - (A2/(3*A3)) Else If hc2=0 And gc2=0 And fc2=0 Then Rx(0) =-((A0/A3)^0.3333333 ) Else If hc2<0 Or hc2=0 Then ic2= Sqr(((gc2^2)/4) - hc2) jc2 = (ic2)^0.333333 kc2 = ACos (- (gc2 / (2*ic2))) Lc2 = -jc2 Mc2 = Cos (kc2/3) Nc2 = Sqr( 3) * Sin (kc2/3) Pc2 = -(A2/(3*A3)) Rx(0) = 2*jc2 * Cos(kc2/3) -(A2/(3*A3)) Rx(1) = Lc2 * (Mc2 + Nc2) + Pc2 Rx(2) = Lc2 * (Mc2 - Nc2) + Pc2 EndIf EndIf EndIf End Function
this calculates only the real roots
they are Rx(0), Rx(1), Rx(2)
i am using this code in my AiEditor for Racer
my Site
here a pic of this