Question

What's the formula for finding a cubic polynomial given the sum, sum taken to at a time, and the product of its zeroes ?

Answer 1

Let α, β and ɣ be the roots of the cubic polynomial.
The cubic polynomial with roots α, β and ɣ is
x³ – (α + β + ɣ)x² + (αβ+ βɣ + ɣα)x – (αβɣ) = 0