I don't know if this is the correct forum that I've chosen, I'm new to this. I'm having some trouble with the following question. I would appreciate as much help as possible!!
Let α, β, γ and δ denote the zeros of the quartic polynomial
x^4 + 2x^3 + 3x^2 + 7x − 9.
a)- Write down the four expressions for the elementary symmetric functions in α, β, γ and δ and give their values for this quartic polynomial.
b)- By expressing the following in terms of these elementary symmetric functions, or otherwise, calculate the exact values of α^2+ β^2+ γ^2+ δ^2, and α^3+ β^3+ γ^3+ δ^3, and
(α + β + γ − δ)(α + β − γ + δ)(α − β + γ + δ)(−α + β + γ + δ)