Roots Of Polynomials

Question 1

1/α + 1/β

Answer 1

(α + β)/αβ

Question 2

1/α + 1/β + 1/γ

Answer 2

(βγ + αγ + αβ)/αβγ

Question 3

1/α + 1/β + 1/γ + 1/δ

Answer 3

(Σαβγ)/αβγδ

Question 4

α^2 + β^2

Answer 4

(α + β)^2 -2αβ

Question 5

α^2 + β^2 + γ^2

Answer 5

(α + β + γ)^2 - 2(Σαβ)

Question 6

α^2 + β^2 + γ^2 + δ^2

Answer 6

(α + β + γ + δ)^2 - 2(Σαβ)

Question 7

α^3 + β^3

Answer 7

(α + β)^3 - 3αβ(α + β)

Question 8

α^3 + β^3 + γ^3

Answer 8

(α + β + γ)^3 - 3(Σα)(Σαβ) + 3αβγ