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

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Solving Cubic Equations with Real Coefficients
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If a cubic has real coefficients, what types of roots are possible?

All real or 2 complex conjugates + 1 real

How many complex conjugate roots can a cubic with real coefficients have?

Two

What is C=Q⋅LC = Q \cdot L where CC is cubic?

Quadratic times linear

Given roots 1+i1+i and 33, what is the third root?

1−i1-i

What is (1+i)+(1−i)(1+i)+(1-i)?

22

What is (1+i)⋅(1−i)(1+i) \cdot (1-i)?

22

If S=2S=2 and P=2P=2 are sum and product of roots, what is the quadratic?

z2−2z+2z^2-2z+2

What is the linear factor for root z=3z=3?

(z−3)(z-3)

What is (z−3)(z2−2z+2)(z-3)(z^2-2z+2) expanded?

z3−5z2+8z−6z^3-5z^2+8z-6

What is (5+3i)+(5−3i)(5+3i)+(5-3i)?

1010

What is (5+3i)⋅(5−3i)(5+3i) \cdot (5-3i)?

3434

In z3−kz2+24z+34=0z^3-kz^2+24z+34=0, if −34a=34-34a=34, what is real root aa?

−1-1

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 Flashcards 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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