2. Roots of polynomials Flashcards
1
Q
Roots of Quadratics (2)
A
α + β = -b/a
αβ = c/a
2
Q
Roots of Cubics (3)
A
αβ = /a
α + β + γ = -b/a
αβ + βγ + γα = c/a
αβγ = -d/a
3
Q
One complex root means
A
one other root must it’s conjugate as complex roots always come in pairs
4
Q
a² + b²
A
= (a + bi)(a - bi)
5
Q
(x - z)(x - z*)
A
= x² - 2Re(z)x + |z|²
6
Q
Roots of Quartics (4)
A
α + β + γ + δ = -b/a
αβ + αγ + αδ + βγ + βδ + γδ = c/a
αβγ + αβδ + αγδ + βγδ = -d/a
αβγδ = e/a