g(x) is a quadratic function given by:
g(x) = x² + 12x + 30.

Determine all possible real roots of this equation:
g(g(g(g(g(x))))) = 0

(In reply to re: Jer seems right; I must have erred somewhere by Daniel)

Thanks, Daniel for spotting my bug. Note the 30 in lines 160 and 170, replacing the C:

 10      gosub *Solve(1,12,30)
 20
 30      end
 40
 50      *Solve(A,B,C)
 60        local Discr,S1,S2
 70        Lvl=Lvl+1
 80        Discr=B*B-4*A*C
 90     '  print Lvl,A;B;C,Discr
100           Vr=sqrt(Discr)
110           S1=(-B+Vr)/(2*A)
120           S2=(-B-Vr)/(2*A)
130           if Lvl=5 then
140            :print S1:print S2:Ct=Ct+1:if Ct@20=0 then stop:endif
150          :else
160            :gosub *Solve(A,B,30-S1)
170            :gosub *Solve(A,B,30-S2)
180          :endif
190        Lvl=Lvl-1
200      return

All the solutions:

-4.9424102657581145658
-7.0575897342418854341
-6.0+1.057589734241885434#i
-6.0-1.057589734241885434#i
-5.2521711272042841685+0.7478288727957158314#i
-6.7478288727957158314-0.7478288727957158314#i
-5.2521711272042841685-0.7478288727957158314#i
-6.7478288727957158314+0.7478288727957158314#i
-5.0229144907398708858+0.4047220695337678307#i
-6.9770855092601291141-0.4047220695337678307#i
-6.4047220695337678307+0.9770855092601291141#i
-5.5952779304662321692-0.9770855092601291141#i
-5.0229144907398708858-0.4047220695337678307#i
-6.9770855092601291141+0.4047220695337678307#i
-5.5952779304662321692+0.9770855092601291141#i
-6.4047220695337678307-0.9770855092601291141#i
-4.9627315559499944232+0.2063255218142009457#i
-7.0372684440500055767-0.2063255218142009457#i
-6.2063255218142009457+1.0372684440500055767#i
-5.7936744781857990542-1.0372684440500055767#i
-5.4124346249080965193+0.8793537263052523328#i
-6.5875653750919034806-0.8793537263052523328#i
-5.120646273694747667-0.5875653750919034806#i
-6.8793537263052523328+0.5875653750919034806#i
-4.9627315559499944232-0.2063255218142009457#i
-7.0372684440500055767+0.2063255218142009457#i
-5.7936744781857990542+1.0372684440500055767#i
-6.2063255218142009457-1.0372684440500055767#i
-5.120646273694747667+0.5875653750919034806#i
-6.8793537263052523328-0.5875653750919034806#i
-6.5875653750919034806+0.8793537263052523328#i
-5.4124346249080965193-0.8793537263052523328#i

the first two being real:

-4.9424102657581145658 and -7.0575897342418854341, the first of which was found by Jer.

Edited on November 6, 2013, 9:59 am

Posted by Charlie on 2013-11-06 09:58:00