🚀 go-pugleaf

Why should we teach the square root of large numbers? It is in the
calculator. The same with the zeros of the polynomials. Show the
zeros of the 2nd order polynomial (quadratic equation) and the rest 
is in the computer.

	Zeros of:  a*z^5+b*z^4+c*z^3+d*z^2+e*z+f

Consider:  a*z^5+b*z^4+c*z^3+d*z^2+e*z+f

where  z=x+iy ,  a,b,c,d,e, f -   are real numbers.

Running the following MATLAB program for  particular values of a,b,c,d,e,f

the location of zeros is shown in a x,y -plane of an orthogonal coordinate
system.   An example:
                          *** PROGRAM IS COPYRIGHTED ***
x=-3:.03:3;
y=-3:.03:3;           
[X,Y] = meshgrid(x,y);
a=1; b=0; c=1; d=0; e=0; f=-32;

Z=sqrt((a*(X.^5-10*(X.^3).*(Y.^2)+5*X.*(Y.^4))+b*(X.^4-6*(X.^2).*(Y.^2)+Y.
^4)+c*(X.^3-3*X.*(Y.^2))+d*(X.^2-Y.^2)+e*X+f).^2+(a*(5*(X.^4).*Y-10*(X.^2).
*(Y.^3)+Y.^5)+b*(4*(X.^3).*Y-4*X.*(Y.^3))+c*(3*(X.^2).*Y-Y.^3)+d*(2*(X.*Y))
+e*Y).^2).*(+sin(atan((a*
(5*(X.^4).*Y-10*(X.^2).*(Y.^3)+Y.^5)+b*(4*(X.^3).*Y-4*X.*(Y.^3))+c*(3*(X.^
2).*Y-Y.^3)+d*(2*X.*Y)+e*Y)./(a*(X.^5-10*(X.^3).*(Y.^2)+5*X.*(Y.^4))+b*(X.^
4-6*(X.^2).*(Y.^2)+Y.^4)+c*(X.^3-3*X.*(Y.^2))+d*(X.^2-Y.^2)+e*X+f)))+cos(at
an((a*(5*(X.^4).*Y-10*(X.
^2).*(Y.^3)+Y.^5)+b*(4*(X.^3).*Y-4*X.*(Y.^3))+c*(3*(X.^2).*Y-Y.^3)+d*(2*X.
*Y)+e*Y)./(a*(X.^5-10*(X.^3).*(Y.^2)+5*X.*(Y.^4))+b*(X.^4-6*(X.^2).*(Y.^2)+
Y.^4)+c*(X.^3-3*X.*(Y.^2))+d*(X.^2-Y.^2)+e*X+f))));
c=contour(X,Y,Z,0:400:800);
clabel(c,'manual');
%diary 'nina'
%Y
%diary 'toma"
%X

If there is an interest in the results where MATLAB software is not
available
please request a fax- transmission. 

tleko@aol.com