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diff --git a/50/CH2/EX2.15/ex_15.sce b/50/CH2/EX2.15/ex_15.sce
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+                                   // The equation cos(x)-x*%e^x==0 has  real roots.
+                                   // the graph of this function can be observed here.
+xset('window',8);                                   
+x=-1:.001:2;                                             // defining the range of x.
+deff('[y]=f(x)','y=cos(x)-x*%e^x');                  //defining the cunction.
+deff('[y]=fp(x)','y=-sin(x)-x*%e^x-%e^x');
+deff('[y]=fpp(x)','y=-cos(x)-x*%e^x-2*%e^x');
+y=feval(x,f);
+ 
+a=gca(); 
+ 
+a.y_location = "origin";
+ 
+a.x_location = "origin"; 
+plot(x,y)                                                  // instruction to plot the graph 
+title(' y = cos(x)-x*%e^x')
+
+// from the above plot we can infre that the function has root between   
+// the interval (0,1)
+
+
+// a=0;b=1,
+
+
+
+            // solution by chebyshev with a permissible error of 10^-15.
+
+// we call a user-defined function 'chebyshev' so as to find the approximate 
+// root of the equation within the defined permissible error limit.  
+
+chebyshev(1,f,fp)
+
+
+
+// hence the approximate root witin the permissible error of 10^-15 is 
+\ No newline at end of file