Question

Write code to approximate √25 3 by applying the a) bisection method and b) false position method to the equation ?^3 = 25. Code the algorithms. Choose the starting guesses. Determine the result accurate to at least to 5 sig figs.

Answer 1

You havent specified the format in which cody expects the code to be. So here is a code which asks for a and b and displays the root with a suitable message

a)Bisection

clear
f=@(x)x^3-25;
a=input('Enter a of interval[a,b]:');
b=input('Enter b of interval[a,b]:');
if f(a)*f(b)>=0
fprintf('Wrong choice of interval!!Exiting\n')
return
else
c0=0;
c=100;
while(abs(c-c0)>10^-5)
c0=c;
c=(a+b)/2;
if f(a)*f(c)<0
b=c;
else
a=c;
end
end
end
fprintf('Root found=%.5f\n',c)

b)false position

clear
f=@(x)x^3-25;
a=input('Enter a of interval[a,b]:');
b=input('Enter b of interval[a,b]:');
if f(a)*f(b)>=0
fprintf('Wrong choice of interval!!Exiting\n')
return
else
c0=0;
c=100;
while(abs(c-c0)>10^-5)
c0=c;
c=(a+b)/2;
if f(a)*f(c)<0
b=c;
else
a=c;
end
end
end
fprintf('Root found=%.5f\n',c)