Jeremiah Oeltjen

Finding a polynomial with given roots

This is for future reference because it took me forever to remember how to do it the other day.

The problem is to find an n^th degree polynomial that satisfies a specific set of conditions:

• n = 3
• 2 and 4i are zeros
• f(2) = -51

First and foremost, since this is a 3^rd degree polynomial we need three roots, but are given only two. The third one comes from the fact that imaginary roots come in conjugate pairs. This means that since 4i is a root -4i must also be. Now we have three roots.

Now, those three roots can be used to determine three linear factors of the polynomial in the form (x - a) along with an unknown factor, a:

f(x) = a(x - 2)(x - 4i)(x + 4i)

f(x) = a(x - 2)(x - 4i)(x + 4i)

New Host

I just finished moving my site over to a new hosting company: A2 Hosting. I only signed up for one month while I tested the water, but it looks like it'll do everything that I need. The big features I needed were mod_rewrite, PHP, MySQL. I also have some Redirect and ForceType directives in a few of my .htaccess files which I am happy they still work. It just took a little bit of reconfiguring to get Movable Type, MediaWiki, and Gallery running again.