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// The equation x^3-5*x+1==0 has real roots.
// the graph of this function can be observed here.
xset('window',10);
x=-2:.01:4; // defining the range of x.
deff('[y]=f(x)','y=x^3-5*x+1'); //defining the cunction.
y=feval(x,f);
a=gca();
a.y_location = "origin";
a.x_location = "origin";
plot(x,y) // instruction to plot the graph
title(' y = x^3-5*x+1')
// from the above plot we can infre that the function has roots between
// the intervals (0,1),(2,3).
// since we have been asked for the smallest positive root of the equation,
// we are intrested on the interval (0,1)
//sollution by muller method to 3 iterations.
muller3(0,.5,1,f)
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