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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',2);                                   
+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)
+// a=0;b=1,
+
+// we call a user-defined function 'bisection' so as to find the approximate 
+// root of the equation with a defined permissible error.  
+
+bisection(0,1,f)
+
+// since in the example 2.3 we have been asked to perform 5 itterations
+// the approximate  root after 5 iterations can be observed.
+
+
+
+bisection5(0,1,f)  
+
+
+// hence the approximate root after 5 iterations is 0.203125 witin the permissible error of 10^-4,
+\ No newline at end of file