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