plumiComplex roots of polynomials: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on B.2 Complex roots of polynomials, 2019–2025, 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 12 questions on Complex roots of polynomials, as a list
- June 2025, Paper 1, Q13 (7 marks): The function f is defined by f ( ) = + + + 3 2 4 92 z z rz z s where r and s are real numbers. One of the roots of the equation f ( ) = 0 z is i −+ 4 3 13 (a) F
- June 2025, AS Paper 1, Q2 (1 mark): The complex number 3 + 5i is a root of the quadratic equation z2 + az + b = 0 where a and b are real constants. Find the other root of the equation. Circle your
- June 2024, Paper 2, Q4 (1 mark): The function f is a quartic function with real coefficients. The complex number 5i is a root of the equation f(x) = 0 Which one of the following must be a facto
- June 2024, Paper 2, Q11 (3 marks): Latifa and Sam are studying polynomial equations of degree greater than 2, with real coefficients and no repeated roots. Latifa says that if such an equation ha
- June 2023, AS Paper 1, Q12 (13 marks): (a) Show that (1 + i)൯ = – 4 [3 marks] 12 (b) The function f is defined by f (z) = z4 + 3z2 – 6z + 10 z ℂ 12 (b) (i) Show that (1 + i) is a root of f (z) = 0 [2
- June 2022, Paper 1, Q5 (6 marks): It is given that z = − 3 2 + i 11 p 2 is a root of the equation z4 − 3z3 − 5z2 + kz + 40 = 0 where k is a real number. 5 (a) Find the other three roots. [5 mark
- November 2021, Paper 1, Q2 (1 mark): Given that z = 1 − 3i is one root of the equation z2 + pz + r = 0 , where p and r are real, find the value of r. Circle your answer. [1 mark] −8 −2 6 10
- November 2021, AS Paper 1, Q8 (6 marks): Stephen is correctly told that (1 + i) and −1 are two roots of the polynomial equation z3 − 2iz2 + pz + q = 0 where p and q are complex numbers. 8 (a) Stephen s
- November 2020, Paper 1, Q4 (6 marks): It is given that 1 − 3i is one root of the quartic equation z4 − 2z3 + pz2 + rz + 80 = 0 where p and r are real numbers. 4 (a) Express z4 − 2z3 + pz2 + rz + 80
- November 2020, AS Paper 1, Q2 (1 mark): Given that 1 − i is a root of the equation z3 − 3z2 + 4z − 2 = 0 , find the other two roots. Tick (3) one box. [1 mark] −1 + i and −1 1 + i and 1 −1 + i and 1 1
- June 2019, Paper 2, Q12 (5 marks): Abel and Bonnie are trying to solve this mathematical problem: z = 2 − 3i is a root of the equation 2z3 + mz2 + pz + 91 = 0 Find the value of m and the value of
- June 2019, AS Paper 1, Q14 (7 marks): The graph of y = x3 − 3x is shown below. x y y = x3 – 3x O The two stationary points have x-coordinates of −1 and 1 The cubic equation x3 − 3x + p = 0 where p i
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