Question

Determine the real root of f ( x )=−12−21 x+18 x
2−2.75 x
3
. Using bisection to locate the
root. Employ initial guesses of xL=−1 and xU=0 and iterate until the estimated error falls
below a level of 1%.

Answer 1

Answer:

clc

f = @(x) -12-(21*x)+(18*x^2)-(2.75*x^3);

a=-1;

b=0;

p=a;

%Bisection Method

while (abs(f(p))>0.01)

p = (a+b)/2;

if f(p) == 0

break;

end

if f(a)*f(p)<0

b=p;

else

a = p;

end

end

fprintf('The final root through bisection method is %f\n',p);

%False Position Method

p=a;

while (abs(f(p))>0.01)

p = (a*f(b)-b*f(a))/(f(b)-f(a));

if f(p) == 0

break;

end

if f(a)*f(p)<0

b=p;

else

a = p;

end

end

fprintf('The final root through False Position method is %f\n',p);