plumiComplex roots of polynomials: OCR MEI A‑Level Further Maths questions
OCR MEI 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 13 questions on Complex roots of polynomials, as a list
- June 2025, Core Pure, Q12 (8 marks): In this question you must show detailed reasoning. are a, 2 4 3 2 The roots of the equation z z cz dz 18 0 a , b and - . - + + + = b Determine, in any order, th
- June 2025, AS Core Pure, Q8 (8 marks): 2 8 The three distinct roots of the equation z 4 z pz q 0 , where p and q are real, are drawn on - + + = an Argand diagram. The three points which represent the
- June 2024, AS Core Pure, Q1 (4 marks): + 1 The quadratic equation x ax b 0 , where a and b are real constants, has a root 2 3 i. + = - (a) Write down the other root. [1] (b) Hence or otherwise determ
- June 2024, AS Core Pure, Q4 (7 marks): In this question you must show detailed reasoning. 3 2 The roots of the cubic equation x 3 x 19 x 17 0 are a, b and c. - + - = 1 a - 1 b - (a) Find a cubic equa
- June 2023, AS Core Pure, Q3 (6 marks): In this question you must show detailed reasoning. 3 2 The function f (z) is given by ( ) f z 2 z 7 z 16 z 15 . = - + - 3a k, find the roots of f (z) = 0. By fi
- June 2022, Core Pure, Q10 (10 marks): The equation 4 3 2 4 x 16 x ax bx 6 0 , + + + + = where a and b are real, has roots a, 2 a , b and 3b. (a) Given that ,0 determine all 4 roots. [6] 1 b (b) Dete
- June 2022, AS Core Pure, Q4 (6 marks): In this question you must show detailed reasoning. where k is a constant, has roots a, 1 3 2 z z kz The equation 2 3 0 , a and b. + + + = [6] Determine the root
- November 2021, Core Pure, Q8 (9 marks): , where p and q are constants, has roots a, -a, b and 1 4 3 2 8 The equation x 4 4 x px qx 9 0 b . - + + - = (a) Determine the exact roots of the equation. [5]
- November 2021, AS Core Pure, Q8 (7 marks): In this question you must show detailed reasoning. a . Given that 3 2 The equation x kx 15 x 25 0 has roots a, b and b 2 0 , find, in any order, + + - = a • the
- November 2020, AS Core Pure, Q7 (7 marks): 3 2 7 In the quartic equation x 2 20 x ax bx 250 0 , the coefficients a and b are real. One root - + + + = of the equation is 2 + . i Find the other roots. [7]
- June 2019, Core Pure, Q8 (8 marks): In this question you must show detailed reasoning. 1 3 2 The roots of the equation x x kx 2 0 are , and b. - + - = a a (a) Evaluate, in exact form, the roots of
- June 2019, AS Core Pure, Q8 (11 marks): In this question you must show detailed reasoning. 4 3 2 You are given that i is a root of the equation z 2 z 3 z az b 0 , where a and b are real - + + + = cons
- June 2018, AS Core Pure, Q4 (5 marks): [5] Find a cubic equation with real coefficients, two of whose roots are 2 - i and 3.
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