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// The equation 27*x^5+27*x^4+36*x^3+28*x^2+9*x+1==0 has real roots.
// the graph of this function can be observed here.
xset('window',26);
x=-2:.001:3; // defining the range of x.
deff('[y]=f(x)','y=27*x^5+27*x^4+36*x^3+28*x^2+9*x+1'); //defining the cunction.
deff('[y]=fp(x)','y=27*5*x^4+27*4*x^3+36*3*x^2+28*2*x+9');
deff('[y]=fpp(x)','y=27*5*4*x^3+27*4*3*x^2+36*3*2*x+28*2');
y=feval(x,f);
a=gca();
a.y_location = "origin";
a.x_location = "origin";
plot(x,y) // instruction to plot the graph
title(' y = 27*x^5+27*x^4+36*x^3+28*x^2+9*x+1')
// solution by newton raphson method as per the equation no. 2.14
newton(-1,f,fp) // calling the user defined function
newton4(-1,f,fp)
// solution by newton raphson method as per the equation no. 2.63
newton63(-1,f,fp,fpp) // calling the user defined function
// solution by the secant method defined to satisfy the equation no.2.64.
secant64(0,-1,f,fp)
// solution by the secant method defined to satisfy the equation no.2.65.
secant65(0,-.5,f)
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