Relationship between roots and coefficients (HSC SSCE Mathematics Extension 1): Flashcards
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What is a polynomial equation?
What is a polynomial equation?
It looks like ax^n + bx^{n-1} + ... + k = 0.
What is the sum of roots in a quadratic polynomial?
What is the sum of roots in a quadratic polynomial?
α + β = -b/a.
What is the product of roots in a quadratic polynomial?
What is the product of roots in a quadratic polynomial?
αβ = c/a.
What is the sum of roots in a cubic polynomial?
What is the sum of roots in a cubic polynomial?
α + β + γ = -b/a.
What is the product of roots in a cubic polynomial?
What is the product of roots in a cubic polynomial?
αβγ = -d/a.
What is the sum of roots in a quartic polynomial?
What is the sum of roots in a quartic polynomial?
α + β + γ + δ = -b/a.
What is the product of roots in a quartic polynomial?
What is the product of roots in a quartic polynomial?
αβγδ = e/a.
What is the identity for α^2 + β^2?
What is the identity for α^2 + β^2?
α^2 + β^2 = (α + β)^2 - 2αβ.
What is the identity for α^3 + β^3?
What is the identity for α^3 + β^3?
α^3 + β^3 = (α + β)^3 - 3αβ(α + β).
What is a limitation of polynomial root properties?
What is a limitation of polynomial root properties?
They need numerical methods for exact roots.