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Pearson Edexcel IAL Mathematics FP1.1.4 Complex solutions of quadratic equations

Practise solving quadratics with real coefficients when roots are complex, then writing each solution in a+ib form.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • solve quadratic factors with negative discriminants and express both roots as a+ib

FP1.1.4 - Complex solutions of quadratic equations question 1

[Maximum number: 4]

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

f(z)=z3−13z2+59z+pp∈Z\mathrm{f}(z)=z^{3}-13 z^{2}+59 z+p \quad p \in \mathbb{Z}

Given that z=3 is a root of the equation f(z)=0

Use algebra to determine the other roots of f(z)=0, giving your answers in simplest form.

On an Argand diagram
- the root z=3 is represented by the point P
- the other roots of f(z)=0 are represented by the points Q and R
- the number z=-9 is represented by the point S

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