Can one edit a built-in Python module?

The math module is a builtin, so short of modifying the Python interpreter itself, I don't think you can modify it. However, writing a module is definitely something you can do.

If you structure your files like this:

somefolder
    mymath.py
    myprogram.py

...you could simply do import mymath inside myprogram.py, and use any functions or classes inside mymath.py as normal.

So if mymath.py looks like this:

def quadratic(a, b, c):
    # blah blah blah

You could do the below inside myprogram.py

import mymath

print mymath.quadratic(1, 2, 3)

If you want the module you've written available for any program, you could either copy-and-paste it into the folder of any project you're working on, or add it to your PATH. (For example, you could include mymath.py inside the site-packages folder, which is located at C:\Python27\Lib\site-packages on my computer). Once you do that, you should be able to do import mymath without ever having to copy-and-paste anything.

As a side-note, numpy has a pretty comprehensive set of math and science related functions that you could check out. It's pretty much the de-facto standard for numerical computation in Python, afaik.