Roots of Polynomials Flashcards
(18 cards)
1
Q
What are the roots of a quadratic?
A
α & β
2
Q
α+β = ?
A
-b/a
3
Q
αβ = ?
A
c/a
4
Q
What are the roots of a cubic?
A
α, β & γ
5
Q
-b/aα+β+γ (Σα) = ?
A
b/a
6
Q
αβ+βγ+αγ (Σαβ) = ?
A
c/a
7
Q
αβγ = ?
A
-d/a
8
Q
Cubic in terms of α, β, γ?
A
x^3-(α+β+γ)x^2+(αβ+βγ+αγ)x-αβγ=0
9
Q
1/α+1/β+1/γ =?
A
βγ+αγ+αβ/αβγ
10
Q
What are the roots of a quartic?
A
α, β, γ & δ
11
Q
α+β+γ+δ (Σα) = ?
A
-b/a
12
Q
αβ+αγ+αδ+βγ+βδ+γδ (Σαβ) = ?
A
c/a
13
Q
αβγ+αβδ+αγδ+βγδ (Σαβγ) = ?
A
-d/a
14
Q
αβγδ = ?
A
e/a
15
Q
1/α + 1/β + 1/γ + 1/δ = ?
A
βγδ+αγδ+αβδ+αβγ/αβγδ
16
Q
α^3 + β^3 + γ^3 = ?
A
(α+β+γ)^3-3(α+β+γ)(αβ+βγ+αγ)+3αβγ
17
Q
α^3 + β^3 = ?
A
(α+β)^3-3αβ(α+β)
18
Q
α^2 + β^2 + γ^2 = ?
A
(α+β+γ)^2-2(αβ+βγ+αγ)
