Hey there,

I was reading an article, where the author claims that the following polynomial:

has two roots, first one root is

, which is between 0 and 1, and the other can be expressed as

note that this polynomial is obtained after factoring a second order difference equation with forward and lag operators. Now I have no idea how he arrives at that identity, could anyone explain me the trick behind it?

And while you are at it, could you tell me a similar identity between the roots of the following polynomial:

So for example let

, be the root between 0 and 1 of this polynomial, what is the second root in terms of

?

Thanks a lot

Burak