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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',4);
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 given the interval to be considered as (0,1)
// a=0;b=1,
// Solution by secant method
// since in the example 2.5 we have been asked to perform 4 itterations ,
secant4(0,1,f) // we call a user-defined function 'bisection' so as to find the approximate
// root of the equation with a defined permissible error.
// hence the approximate root occured in secant method after 4 iterations is 0.201640 witin the permissible error of 10^-4,
// solution by regular falsi method
// since in the example 2.5 we have been asked to perform 4 itterations ,
regulafalsi4(0,1,f) // we call a user-defined function 'regularfalsi4' so as to find the approximate
// root of the equation with a defined permissible error.
// hence the approximate root occured in regularfalsi method after 4 iterations is 0.201640 witin the permissible error of 10^-4,
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