Roots of Polynomials Flashcards
1
Q
What are the roots of a quadratic?
A
α & β
2
Q
-b/a (quadratic) = ?
A
α+β
3
Q
c/a (quadratic) = ?
A
αβ
4
Q
What are the roots of a cubic?
A
α, β & γ
5
Q
-b/a (cubic) = ?
A
α+β+γ (= Σα)
6
Q
c/a (cubic) = ?
A
αβ+βγ+αγ (= Σαβ)
7
Q
-d/a (cubic) = ?
A
αβγ (= Σαβ)
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
-b/a (quartic) = ?
A
α+β+γ+δ (= Σα)
12
Q
c/a (quartic) = ?
A
αβ+αγ+αδ+βγ+βδ+γδ (= Σαβ)
13
Q
-d/a (quartic) = ?
A
αβγ+αβδ+αγδ+βγδ (= Σαβγ)
14
Q
e/a (quartic) = ?
A
αβγδ
15
Q
1/α+1/β+1/γ+1/δ = ?
A
βγδ+αγδ+αβδ+αβγ/αβγδ
