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VICSpecialist MathematicsQuick questions

Unit 3: Algebra, number and structure

Quick questions on Solving polynomial equations over C: VCE Specialist Mathematics Unit 3

4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is wrong quadratic factor?
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From roots a±bia \pm bi the real factor is z2−2az+(a2+b2)z^2 - 2az + (a^2 + b^2), not z2+2az+…z^2 + 2az + \dots. Watch the sign.
What is q1?
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A real quartic has roots 1+i1 + i and −3-3. Name one further root it must have. [1 mark]
What is q2?
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Solve z2+4z+13=0z^2 + 4z + 13 = 0 over C\mathbb{C}. [2 marks]
What is q3?
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Given z=1−iz = 1 - i is a root of z3−3z2+4z−2=0z^3 - 3z^2 + 4z - 2 = 0, find all roots. [3 marks]

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