plumiComplex roots of polynomials: OCR A‑Level Further Maths questions
OCR 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, Pure Core 1, Q10 (11 marks): In this question you must show detailed reasoning. (a) Use de Moivre’s Theorem to show that, if cos5 0 , i ! 5 3 tan 10 tan 5 tan - + i i i tan 5 . [4] i / 4 2
- June 2025, Pure Core 2, Q2 (4 marks): 2 2 You are given that 7 5 i is one root of the equation x 10 x 18 x 296 0 . - - + + - = 3 2 (a) Write down another complex root of the equation x 10 x 18 x 296
- June 2024, AS Pure Core, Q9 (8 marks): In this question you must show detailed reasoning. 4 3 2 You are given that a is a real root of the equation x x 3 x 5 x 0 . + + - = You are also given that a 2
- June 2023, Pure Core 1, Q2 (6 marks): In this question you must show detailed reasoning. 4 3 2 The equation z 4 z 9 z 10 z 6 0 has roots a, b, c and d. + + + + = (a) Show that a quartic equation who
- November 2021, Pure Core 1, Q3 (8 marks): 2 3 A function f(z) is defined on all complex numbers z by ( )z f z 3 z kz - where k is a real 5 = - + 2 2 2 constant. The roots of the equation ( )z f 0 are a,
- November 2021, AS Pure Core, Q3 (6 marks): In this question you must show detailed reasoning. 4 3 2 The equation x 7 x 2 x 218 x 1428 0 has a root 3 5i . - - + - = - Find the other three roots of this eq
- November 2020, Pure Core 1, Q9 (9 marks): 2 9 You are given that the cubic equation 2 x px qx 3 0 , where p and q are real numbers, has a + + - = complex root 1 i 2 . a = + (a) Write down a second compl
- June 2019, Pure Core 1, Q3 (4 marks): In this question you must show detailed reasoning. 3 2 You are given that x 2 5 i is a root of the equation x 2 x 21 x 58 0 . = + - + + = Solve the equation. [4
- June 2019, AS Pure Core, Q4 (14 marks): In this question you must show detailed reasoning. 4 3 2 You are given that ( ) f z 4 z 12 z 41 z 128 z 185 and that 2 + is a root of the equation i = - + - + f
- June 2018, AS Pure Core, Q5 (10 marks): In this question you must show detailed reasoning. 3i 3 (i) Express ( 2 ) in the form a + ib. [3] + 3 2 (ii) Hence verify that 2 3i is a root of the equation z
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