2. Roots of polynomials Flashcards

1
Q

Roots of Quadratics (2)

A

α + β = -b/a

αβ = c/a

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2
Q

Roots of Cubics (3)

A

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

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3
Q

One complex root means

A

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

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4
Q

a² + b²

A

= (a + bi)(a - bi)

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5
Q

(x - z)(x - z*)

A

= x² - 2Re(z)x + |z|²

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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

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