How to make this bisection code work for different equations?

Question

I am very new to Mathematica. I have this code of Bisection Method for finding a root of a polynomial.

Bisection[a0_, b0_, e0_, n_] := Module[{},
       a = N[a0];
       b = N[b0];
       e = N[e0];
       i = 0;
       f[x_] := x^2 - x - 12;
       Output = {{i, a, b, }};
       While[i < n,
        c = (a + b)/2;
         Output = Append[Output, {i + 1, a, b, c}];
        If[Sign[f[b]] == Sign[f[c]], b = c, a = c];
        If[(b - a)/2 < e, Print["Condition Exists at ", i + 1, " . "]; 
         Break[] ];
        i = i + 1;
        ];
       Print[NumberForm[TableForm[Output,
          TableHeadings -> {None, {"i", "a{i}", "b{i}", "c{i}"}}], 16]];
       Print["Root p = ", NumberForm[c, 16] ];
       Print[f[x]] ;
       Plot[f[x], {x, -4, 5}]
       ]

Bisection[-4, 2, 10^-5, 10]

It works fine for an example then if I want to use it for other example I have to change the code or copy it for other examples. How can I modify this code so that it takes an equation as an input and I can just used the command (or something like this)

Bisection[x^2 - x - 12,-4, 2, 10^-5, 10]
Bisection[x^3 + x,-4, 2, 10^-5, 10]

which should work for any equation.

Answer 1

Here is you changed code that should work:

poly[x_] = x^2 - x - 12;
Bisection[f_, a0_, b0_, e0_, n_] := Module[{}, a = N[a0];
   b = N[b0];
   e = N[e0];
   i = 0;
   Output = {{i, a, b}};
   While[i < n, c = (a + b)/2;
    Output = Append[Output, {i + 1, a, b, c}];
    If[Sign[f[b]] == Sign[f[c]], b = c, a = c];
    If[(b - a)/2 < e, Print["Condition Exists at ", i + 1, " . "];
     Break[]];
    i = i + 1;];
   Print[
    NumberForm[
     TableForm[Output, 
      TableHeadings -> {None, {"i", "a{i}", "b{i}", "c{i}"}}], 16]];
   Print["Root p = ", NumberForm[c, 16]];
   Print[f[x]];
   Plot[f[x], {x, -4, 5}]];

Now, e.g. for your first polynomial:

Bisection[poly, -4, 2, 10^-5, 10]