plumiRoots of polynomials: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 4.1 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 12 questions on Roots of polynomials, as a list
- June 2025, Core Pure 2, Q6 (8 marks): The quartic equation 2 5 6 0 4 3 2 x Ax Ax x where A is a real constant, has roots , , and (a) Determine the value of 3 3 3 3 (3) Given that 2 2 2 2 3 4
- June 2025, AS Core Pure, Q11 (7 marks): In this question you must show detailed reasoning. f(x) = x 3 – 21x 2 + Ax – 91 where A is a real constant The roots of f(x) = 0 are α, α + 3β and α + 6β where
- June 2024, Core Pure 1, Q2 (8 marks): The roots of the equation 2 3 12 7 0 3 2 x x x are α, β and γ Without solving the equation, (a) write down the value of each of α + β + γ αβ + αγ + βγ αβγ (1) (
- June 2024, AS Core Pure, Q1 (9 marks): The cubic equation 2 3 5 7 0 3 2 x x x has roots α, β and γ. Without solving the equation, determine the exact value of (i) α 2 + β 2 + γ 2 (3) (ii) 3 3 3 α β γ
- June 2023, Core Pure 1, Q1 (5 marks): The cubic equation x 3 – 7x 2 – 12x + 6 = 0 has roots α, β and γ. Without solving the equation, determine a cubic equation whose roots are (α + 2), (β + 2) and
- June 2023, AS Core Pure, Q10 (12 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (i) The quartic equation z 4 + 5z 2 –
- June 2022, Core Pure 2, Q6 (10 marks): The cubic equation 4x 3 + px 2 – 14x + q = 0 where p and q are real positive constants, has roots α, β and γ Given that α 2 + β 2 + γ 2 = 16 (a) show that p = 1
- June 2022, AS Core Pure, Q4 (9 marks): The roots of the quartic equation 3x4 + 5x3 − 7x + 6 = 0 are α, β, γ and δ Making your method clear and without solving the equation, determine the exact value
- November 2021, Core Pure 1, Q3 (6 marks): The cubic equation ax 3 + bx 2 – 19x – b = 0 where a and b are constants, has roots α, β and γ The cubic equation w 3 – 9w 2 – 97w + c = 0 where c is a constant
- November 2020, AS Core Pure, Q9 (6 marks): The cubic equation 3x3 + x2 – 4x + 1 = 0 has roots α, β, and γ. Without solving the cubic equation, (a) determine the value of 1 1 1 α β γ + + (3) (b) find a cu
- June 2019, Core Pure 2, Q2 (8 marks): The roots of the equation x3 – 2x2 + 4x – 5 = 0 are p, q and r. Without solving the equation, find the value of (i) 2 p + 2 q + 2 r (ii) ( p – 4)(q – 4)(r – 4)
- June 2018, AS Core Pure, Q2 (5 marks): The cubic equation z3 – 3z2 + z + 5 = 0 has roots α, β and γ. Without solving the equation, find the cubic equation whose roots are (2α + 1), (2β + 1) and (2γ +
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