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A-LevelFurther MathematicsRoots of polynomial equations9231/12 · Oct/Nov 2017 · Q48 Marks

The cubic equation 2x³ – 3x² + 4x − 10 = 0 has roots α, β and γ.

  1. (i)Find the value of (α + 1)(β + 1)(γ + 1).[4]
  2. (ii)Find the value of (β + γ)(γ + α)(α + β).[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

  1. [1] B1 (Can be awarded in (ii) if not seen here) SOI
  2. [2] M1A1 Multiply out and group for M1
  3. [1] A1FT Alt method: Let x=y-1 M1 Sub and expand 2y³-9y² 16y-19 = 0 M1, A1 Product of roots = 19/2 A1
  4. [1] M1 Alt methods: = (Σα)(Σαβ)–αβγ or Σα² Σα+2αβγ–Σα³
  5. [1] A1
  6. [2] M1A1

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About this question

Topic
Roots of polynomial equations, A-Level Further Mathematics (syllabus 9231). Structured question, 8 marks.
Source
A-Level Further Mathematics, Oct/Nov 2017 Paper 1 Variant 2, question 4.

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