p=[3 5 21 35 48 80 36 60]
p =
1×8
3 5 21 35 48 80 36 60
dp=polyder(p)
%para la derivada
dp =
1×7
21 30 105 140 144 160 36
v=[]
%para guardar las raíces
v = []
x=
i
%numero complejo
x =
0.000000000000000 + 1.000000000000000i
format
long
x=itraiz (p,dp,v,x)
x =
-0.019505851755527 + 1.209362808842653i
x=itraiz (p,dp,v,x)
x =
-0.013694512779891 + 1.307112764618331i
x=itraiz (p,dp,v,x)
x =
-0.008268296223227 + 1.358172594023474i
x=itraiz (p,dp,v,x)
x =
-0.004641219023783 + 1.385265115278417i
x=itraiz (p,dp,v,x)
x =
-0.002483217767170 + 1.399448687240877i
%Sospechamos raíz doble al no apreciar convergencia
%Calculamos ceros de la derivada primera
d2p=polyder(dp);
x=itraiz (dp,d2p,v,x)
x =
-0.000265091247887 + 1.413744152922529i
x=itraiz (dp,d2p,v,x)
x =
-0.000000755481743 + 1.414213281407839i
x=itraiz (dp,d2p,v,x)
x =
-0.000000000000905 + 1.414213562374664i
x=itraiz (dp,d2p,v,x)
x =
-0.000000000000000 + 1.414213562373095i
x=itraiz (dp,d2p,v,x)
x =
-0.000000000000000 + 1.414213562373095i
%Obtenemos -0.000000000000000 + 1.414213562373095i
%comprobamos cero de la derivada primera y de la función
polyval(p,x)
ans =
-7.105427357601002e-15 - 1.261469136533770e-15i
polyval(dp,x)
ans =
2.131628207280301e-14 - 6.786036523265954e-15i
%Es cero de la derivada primera, luego es cero doble de p
%Como es compleja, añadimos sus conjugadas
v=[v;x;conj(x);x;conj(x)]
v =
4×1 complex
-0.000000000000000 + 1.414213562373095i -0.000000000000000 - 1.414213562373095i -0.000000000000000 + 1.414213562373095i -0.000000000000000 - 1.414213562373095i
%Tenemos 4 raíces
x=
i
%numero complejo
x =
0.000000000000000 + 1.000000000000000i
format
long
x=itraiz (p,dp,v,x)
x =
-0.600000000000000 + 2.000000000000005i
x=itraiz (p,dp,v,x)
x =
-0.206894166474524 + 1.591768503573901i
x=itraiz (p,dp,v,x)
x =
0.051515998598106 + 1.729172375086492i
x=itraiz (p,dp,v,x)
x =
0.000644254856565 + 1.730470757492825i
x=itraiz (p,dp,v,x)
x =
-0.000001801091360 + 1.732051443506344i
x=itraiz (p,dp,v,x)
x =
-0.000000000000530 + 1.732050807566546i
x=itraiz (p,dp,v,x)
x =
-0.000000000000000 + 1.732050807568878i
polyval(p,x)
ans =
-7.105427357601002e-15 - 5.740145977397416e-15i
%Se obtiene -0.000000000000000 + 1.732050807568878i
v=[v;x;conj(x)]
v =
6×1 complex
-0.000000000000000 + 1.414213562373095i -0.000000000000000 - 1.414213562373095i -0.000000000000000 + 1.414213562373095i -0.000000000000000 - 1.414213562373095i -0.000000000000000 + 1.732050807568878i -0.000000000000000 - 1.732050807568878i
%Nos falta la raíz real
x=
i
%numero complejo
x =
0.000000000000000 + 1.000000000000000i
format
long
x=itraiz (p,dp,v,x)
x =
-1.666666666666670 - 0.000000000000013i
x=itraiz (p,dp,v,x)
x =
-1.666666666666667 + 0.000000000000000i
x=itraiz (p,dp,v,x)
x =
-1.666666666666667 - 0.000000000000000i
polyval(p,x)
ans =
7.105427357601002e-15 - 2.772264295224331e-43i
%Se obtiene -1.666666666666667
%Las raíces son
v=[v;x]
v =
7×1 complex
-0.000000000000000 + 1.414213562373095i -0.000000000000000 - 1.414213562373095i -0.000000000000000 + 1.414213562373095i -0.000000000000000 - 1.414213562373095i -0.000000000000000 + 1.732050807568878i -0.000000000000000 - 1.732050807568878i -1.666666666666667 - 0.000000000000000i
%Raíces que da roots
roots(p)
ans =
7×1 complex
-1.666666666666668 + 0.000000000000000i -0.000000000000001 + 1.732050807568885i -0.000000000000001 - 1.732050807568885i 0.000000033572273 + 1.414213565895335i 0.000000033572273 - 1.414213565895335i -0.000000033572272 + 1.414213558850850i -0.000000033572272 - 1.414213558850850i