Solving Cubic Equations with Real Coefficients (Leaving Cert Mathematics): Flashcards

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Solving Cubic Equations with Real Coefficients
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Conjugate root theorem: cubics with real coefficients

All real OR 2 complex conjugates + 1 real

Factorisation forms of cubic CC

C=Q⋅LC = Q \cdot L or C=L⋅L⋅LC = L \cdot L \cdot L

Sum of complex conjugates (a+bi)+(a−bi)(a+bi)+(a-bi)

2a2a

Product of (a+bi)(a−bi)(a+bi)(a-bi)

a2+b2a^2 + b^2

Quadratic from sum SS and product PP of roots

z2−Sz+P=0z^2 - Sz + P = 0

Linear factor if root is z=az=a

(z−a)=0(z-a)=0

Given 1 complex root + real coeffs, other complex root?

The conjugate of the given complex root

Method to form cubic from 3 roots

Form quadratic from conjugates, linear from real, expand

How to find unknown coeff in cubic?

Compare coefficients of like terms

Cubic with roots 1+i1+i, 1−i1-i, 33

z3−5z2+8z−6=0z^3-5z^2+8z-6=0

Explore Leaving Cert Mathematics Revision Notes by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

Explore Leaving Cert Mathematics Model Answers by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

Explore Leaving Cert Mathematics Quizzes by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

Explore Leaving Cert Mathematics Exam Questions by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

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