Vieta's formulae for cubics Flashcards
1
Q
A cubic has the form:
A
ax³ + bx² +cx + d = 0
2
Q
A cubic has roots:
A
α, β and γ
3
Q
α + β + γ = ?
A
-b/a
4
Q
αβ + βγ + γα = ?
A
c/a
5
Q
αβγ = ?
A
-d/a
6
Q
α² + β² + γ² = ?
A
(α + β + γ)² - 2(αβ + βγ + γα)
7
Q
α³ + β³ + γ³ = ?
A
(α + β + γ)³ - 3(α + β + γ)(αβ + βγ + γα) + 3(αβγ)
8
Q
α²β² + β²γ² + γ²α² = ?
A
(αβ + βγ + γα)² - 2(α + β + γ)(αβγ)
