## Newton's Relations

Let be the sum of the products of distinct Roots of the Polynomial equation of degree

 (1)

where the roots are taken at a time (i.e., is defined as the Elementary Symmetric Function ) is defined for , ..., . For example, the first few values of are
 (2) (3) (4)

and so on. Then
 (5)

This can be seen for a second Degree Polynomial by multiplying out,

 (6)

so
 (7) (8)

and for a third Degree Polynomial,

 (9)
so

 (10) (11) (12)