Roots of Polynomials

Question 1

Expression for cubics
(x-α)(x-β)(x-γ)

Answer 1

x³ - (α+β+γ)x² + (αβ+αγ+βγ)x - αβγ

α+β+γ = -b/a
αβ+αγ+βγ = c/a
αβγ =-d/a

Question 2

Expression for quartics
(x-α)(x-β)(x-γ)(x-δ)

Answer 2

x4 - (α+β+γ+δ)x³ + (αβ+αγ+αδ+βγ+βδ+γδ)x² - (αβγ+αβδ+αγδ+βγδ)x + αβγδ

sum of singles= -b/a
sum of doubles= c/a
sum of triples= -d/a
quadruples= e/a

Question 3

α³+β³ =

Answer 3

(α+β)³ - 3αβ(α+β)