Solving Equations with Complex Roots (Edexcel A-Level Further Mathematics): Quizzes

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Solving Equations with Complex Roots
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If Δ<0\Delta < 0, what type of roots does a quadratic equation have?

Complex conjugates

What is the discriminant Δ\Delta for x2+4x+5=0x^2 + 4x + 5 = 0?

−4-4

Solve x2+4x+5=0x^2 + 4x + 5 = 0 for xx.

x=−2±ix = -2 \pm i

What are the roots of x2−6x+10=0x^2 - 6x + 10 = 0?

3±i3 \pm i

If z=a+biz = a + bi, what is the complex conjugate z‾\overline{z}?

a−bia - bi

When Δ>0\Delta > 0, what are the roots?

Real and distinct

What is the value of i2i^2?

−1-1

Complex roots of quadratic equations always occur as what?

Conjugate pairs

If Δ=0\Delta = 0, what type of roots exist?

Real and equal

Which technique can solve higher-order polynomials?

Synthetic division

Explore Edexcel A-Level Further Mathematics Revision Notes by Topics

Complex Numbers & Argand Diagrams

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Complex Numbers & Argand Diagrams

Exponential Form & de Moivre's Theorem

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Complex Numbers & Argand Diagrams

Exponential Form & de Moivre's Theorem

Explore Edexcel A-Level Further Mathematics Exam Questions by Topics

Complex Numbers & Argand Diagrams

Exponential Form & de Moivre's Theorem

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