Let and be the roots of . Compute , , , and .
We can readily see that, without loss of generality, and .
Let and be the elementary symmetric polynomials in two variables. Our task is to evaluate the (symmetric) polynomials , , , and at . Note that these are precisely , , , and .
We can directly compute and easily enough. Now and .
Note that once and are computed, all other symmetric combinations of and can be computed entirely inside .