Pure 4: Roots Of Polynomials

Question 1

Roots of Quadratics (2)

Answer 1

α + β = -b/a

αβ = c/a

Question 2

Roots of Cubics (3)

Answer 2

α + β + λ = -b/a
αβ + βλ + λα = c/a
αβλ = -d/a

Question 3

Roots of Quartics (4)

Answer 3

α + β + λ + δ = Σα = -b/a
αβ + βλ + λα + αδ + βδ + λδ = Σαβ = c/a
αβλ + αβδ + βλδ + αλδ = Σαβλ = -d/a
αβλδ = e/a

Question 4

Quadratic Reciprocals

Answer 4

1/α + 1/β = α+β / αβ

Question 5

Cubic Reciprocals

Answer 5

1/α + 1/β + 1/λ = αβ+βλ+λα / αβλ

Question 6

Quartic Reciprocals

Answer 6

1/α + 1/β + 1/λ + 1/δ = Σαβλ / αβλδ

Question 7

Sums of Squares - Quadratics

Answer 7

α^2 + β^2 = (α+β)^2 - 2αβ

Question 8

Sums of Squares - Cubics

Answer 8

α^2 + β^2 + λ^2 =(α+β+λ)^2 - 2(αβ+βλ+λα)

Question 9

Sums of Squares - Quartics

Answer 9

α^2 + β^2 + λ^2 + δ^2 =(Σα)^2 - 2(Σαβ)

Question 10

Sums of Cubes - Quadratics

Answer 10

α^3 + β^3 = (α+β)^3 - 3αβ(α+β)

Question 11

Sums of Cubes - Cubics

Answer 11

α^3 + β^3 + λ^3 = (Σα)^3 - 3(Σα)(Σαβ) + 3αβλ