Question

Consider the following polynomial equation: ax3 bx2 cx d 0 Write a program that allows the user to enter the coefficients a,b,c and d and the search range needed for the Bisection method. The program should stop when the maximum error is less than 0.01. The program should display the root and also have a condition to stop when no roots are found in the range.

PLEASE USE MATLAB.

THANK YOU!

Answer 1

a=input('enter coefficient a: ');
b=input('enter coefficient b: ');
c=input('enter coefficient c: ');
d=input('enter coefficient d: ');
fn = @(x) a*x^3+b*x^2+c*x+d;
a=input('enter lower value of interval: ');
b=input('enter upper value of interval: ');
%to check if the solution exits in the given interval
an=fn(a)*fn(b);
if an>0
    fprintf('the root does not exit between given range');
else
    fprintf('the root lies between the interval and \n');
end
x1=a;
x2=b;
error=2;
while error>=0.01
    x0=(x1+x2)/2;
    an=fn(x0);
    error=abs(0-an);
    if fn(x0)<0
        x1=x0;
        x2=x2;
    else
        x1=x1;
        x2=x0;
    end
end
fprintf('the root is= %f\n',x0);

a) to check for solution in the range

Command Window >bisecc enter coefficient a: 2 enter coefficient b: 3 enter coefficient c: 4 enter coefficient d: 5 enter lower value of interval: -3 enter upper value of interval: 1 the root lies between the interval and the root is= -1.371094 >>

b) to check for condition if root does not lie in the range

> bisecc enter coefficient a: 2 enter coefficient b 3 enter coefficient c: 4 enter coefficient d: 5 enter lower value of interval: 1 enter upper value of interval: 3 f the root does not exit between given range