Forming Quadratic Equations when Given Roots (Leaving Cert Mathematics): Flashcards

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Forming Quadratic Equations when Given Roots
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Theorem for complex roots with real coefficients

Conjugate root theorem

If quadratic coefficients are real, what are the roots?

Both real or complex conjugates

If (−3−2i)(-3-2i) is a root, what is the other root?

(−3+2i)(-3+2i)

Formula to form quadratic from roots

z2−Sz+P=0z^2-Sz+P=0

What does SS represent in z2−Sz+P=0z^2-Sz+P=0?

Sum of the roots

What does PP represent in z2−Sz+P=0z^2-Sz+P=0?

Product of the roots

Conjugate of −2+5i-2+5i

−2−5i-2-5i

Sum of roots −2+5i-2+5i and −2−5i-2-5i

−4-4

Product of (−2+5i)(-2+5i) and (−2−5i)(-2-5i)

2929

Quadratic with roots −2+5i-2+5i and −2−5i-2-5i

z2+4z+29=0z^2+4z+29=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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