Core Pure - Roots of Polynomials

Question 1

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

Answer 1

-b/a

Question 2

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

Answer 2

c/a

Question 3

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

Answer 3

-d/a

Question 4

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

Answer 4

e/a

Question 5

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

Answer 5

1/α + 1/β = Σα/Σαβ

Question 6

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

Answer 6

1/α + 1/β + 1/γ = Σαβ/Σαβγ

Question 7

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

Answer 7

1/α + 1/β + 1/γ + 1/δ = Σαβγ/Σαβγδ

Question 8

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

Answer 8

(Σα)² - 2(Σαβ)

Question 9

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

Answer 9

α³ + β³ = (Σα)³ - 3αβ(Σα)

Question 10

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

Answer 10

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

Question 11

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

Answer 11

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

Question 12

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

Answer 12

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