2. Roots of polynomials

Question 1

Roots of Quadratics (2)

Answer 1

α + β = -b/a

αβ = c/a

Question 2

Roots of Cubics (3)

Answer 2

αβ = /a
α + β + γ = -b/a
αβ + βγ + γα = c/a
αβγ = -d/a

Question 3

One complex root means

Answer 3

one other root must it’s conjugate as complex roots always come in pairs

Question 4

a² + b²

Answer 4

= (a + bi)(a - bi)

Question 5

(x - z)(x - z*)

Answer 5

= x² - 2Re(z)x + |z|²

Question 6

Roots of Quartics (4)

Answer 6

α + β + γ + δ = -b/a
αβ + αγ + αδ + βγ + βδ + γδ = c/a
αβγ + αβδ + αγδ + βγδ = -d/a
αβγδ = e/a