Use Matlab Please!!! One method for finding a root of a function is the bisectio

Question

Use Matlab Please!!!

One method for finding a root of a function is the bisection method. Here is a nice writeup on the bisection method: http://www.mathwarehouse.com/calculus/continuity/continuity-bisection-method.php (Links to an external site.)Links to an external site.

Write a function bisect( ) that finds the root of a polynomial ax3+bx2+cx+d over an interval [A,B]. The function takes as input the coefficients a, b, c, d, and the interval limits A and B. The function returns as output the value of the root over the interval [A,B], if it exists. The function also returns as output a message (flag) that informs the user if no roots exist over the interval [A,B]. It should be clear that you cannot use any of MATLAB's built-in root finding functions to do this problem. Use the bisection method.

a = -1;

b = 1;

c = -1;

d = 10;

A = 0;

B = 5;

[root,flag] = bisect(a,b,c,d,A,B)

Explanation / Answer

function [root,flag] = bisect(a,b,c,d,A,B)
   fun = @(a,b,c,d,x) a*(x^3) + b*(x^2) + c*x + d;
   if fun(a,b,c,d,A) * fun(a,b,c,d,B) > 0
      flag = 0;
      root = 0;
      return;
    end
   if fun(a,b,c,d,A) > fun(a,b,c,d,B)
      t = A;
      A = B;
      B = t;
   end
   root = (A + B)/2;
   while abs(fun(a,b,c,d,root)) > 0.001
      if fun(a,b,c,d,root) > 0
         B = root;
      else
         A = root;
      end
      root = (A + B)/2;
   end
   flag = 1;
end

flag 0 is failure flag

flag 1 is success

I hope this helped you. :)

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