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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)

+