Roots of Polynomials

If α and β are roots of the equation ax² + bx + c = 0, then Σα =

−b/a

If α and β are roots of the equation ax² + bx + c = 0, then αβ =

c/a

If α, β and γ are roots of the equation ax³ + bx² + cx + d = 0, then Σα =

−b/a

If α, β and γ are roots of the equation ax³ + bx² + cx + d = 0, then Σαβ =

c/a

If α, β and γ are roots of the equation ax³ + bx² + cx + d = 0, then αβγ =

−d/a

If α, β, γ and δ are roots of the equation ax⁴ + bx³ + cx² + dx + e = 0, then Σα =

−b/a

If α, β, γ and δ are roots of the equation ax⁴ + bx³ + cx² + dx + e = 0, then Σαβ =

c/a

If α, β, γ and δ are roots of the equation ax⁴ + bx³ + cx² + dx + e = 0, then Σαβγ =

−d/a

If α, β, γ and δ are roots of the equation ax⁴ + bx³ + cx² + dx + e = 0, then αβγδ =

e/a

1/α + 1/β

Σα / αβ

1/α + 1/β + 1/γ

Σαβ / αβγ

1/α + 1/β + 1/γ + 1/δ

(Σαβγ) / αβγδ

α² + β²

(Σα)² − 2(Σαβ)

α² + β² + γ²

(Σα)² − 2(Σαβ)

α² + β² + γ² + δ²

(Σα)² − 2(Σαβ)

α³ + β³

(Σα)³ − 3(Σα)(Σαβ)

α³ + β³ + γ³

(Σα)³ − 3(Σα)(Σαβ) + 3αβγ