# Core Pure - Roots of Polynomials Flashcards

What is Σα equal to in a polynomial expression? (quadratics, cubics and quartics)

-b/a

What is Σαβ equal to in a polynomial expression? (quadratics, cubics, and quartics)

c/a

What is Σαβγ equal to in a polynomial expression? (cubics, and quartics)

-d/a

What is Σαβγδ equal to in a polynomial expression? (quartics)

e/a

What is the rule for the sum of recpirocals of quadratic roots (1/α + 1/β)?

1/α + 1/β = Σα/Σαβ

What is the rule for the sum of reciprocals of cubic roots (1/α + 1/β + 1/γ)?

1/α + 1/β + 1/γ = Σαβ/Σαβγ

What is the rule for the sum of reciprocals of quartic roots (1/α + 1/β + 1/γ + 1/δ)?

1/α + 1/β + 1/γ + 1/δ = Σαβγ/Σαβγδ

What is the rule for sum of squares of roots of a polynomial expression (α² + β² + γ² + δ²)?

(Σα)² - 2(Σαβ)

What is the rule for sum of cubes of roots of a quadratic (α³ + β³)?

α³ + β³ = (Σα)³ - 3αβ(Σα)

What is the rule for sum of cubes of roots of a cubic (α³ + β³ + γ³)?

α³ + β³ + γ³ = (Σα)³ - 3(Σα)(Σαβ) + 3αβγ

What is the rule for the sum of squares of root pairs of a cubic (αβ)² + (αγ)² + (βγ)²?

(αβ)² + (αγ)² + (βγ)² = (Σαβ)² - 2αβγ(Σα)

What is the rule for the sum of cubes of root pairs of a cubic (αβ)³ + (αγ)³ + (βγ)³?

(αβ)³ + (αγ)³ + (βγ)³ = (Σαβ)³ - 3(Σα)(Σαβ)(αβγ) + 3(αβγ)²