Suppose is a polynomial of degree with roots
(not necessarily distinct). For
, define by
For example,
Then writing as
we find that
For example, if is a polynomial of degree 1, then
and clearly
.
If is a polynomial of degree 2, then
and
and
. Notice that both of these formulas can be determined from the quadratic formula.
More intrestingly, if
, then
,
, and
.
