plumiComplex roots of polynomials: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 2.2 Complex roots of polynomials, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 10 questions on Complex roots of polynomials, as a list
- June 2025, Core Pure 1, Q6 (5 marks): f (z) = z3 + az2 + bz + c where a, b and c are real constants The roots of the equation f (z) = 0 are z1, z2 and z3 When plotted on an Argand diagram, the point
- June 2025, AS Core Pure, Q2 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. f(z) = 4z 3 – 12z 2 – 95z + 3
- June 2024, Core Pure 1, Q1 (9 marks): f(z) = z z az bz 4 3 2 6 145 where a and b are real constants. Given that 2 + 5i is a root of the equation f(z) = 0 (a) determine the other roots of the equatio
- June 2023, Core Pure 2, Q8 (11 marks): Given that a cubic equation has three distinct roots that all lie on the same straight line in the complex plane, (a) describe the possible lines the roots can
- June 2023, AS Core Pure, Q2 (7 marks): f (z) = z 3 + az 2 + bz + 175 where a and b are real constants Given that –3 + 4i is a root of the equation f(z) = 0 (a) determine the value of a and the value
- June 2022, Core Pure 1, Q1 (6 marks): f(z) = z3 + az + 52 where a is a real constant Given that 2 – 3i is a root of the equation f(z) = 0 (a) write down the other complex root. (1) (b) Hence (i) sol
- November 2020, Core Pure 1, Q1 (10 marks): f ( z ) = 3z3 + pz2 + 57z + q where p and q are real constants. Given that 3 2 2 − i is a root of the equation f(z) = 0 (a) show all the roots of f(z) = 0 on a
- November 2020, AS Core Pure, Q7 (6 marks): f(z) = z4 + az3 + bz2 + cz + d where a, b, c and d are real constants. The equation f(z) = 0 has complex roots z1, z2, z3 and z4 When plotted on an Argand diagr
- June 2019, Core Pure 1, Q1 (9 marks): I z z4 + az3 + bz2 + cz + d where a, b, c and d are real constants. *LYHQWKDWíLDQGíLDUHWZRURRWVRIWKHHTXDWLRQI z D VKRZDO
- June 2018, AS Core Pure, Q7 (7 marks): f (z) = z3 + z2 + pz + q where p and q are real constants. The equation f (z) = 0 has roots z1 , z2 and z3 When plotted on an Argand diagram, the points represe
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