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A-LevelFurther MathematicsRoots of polynomial equations9231/12 · May/June 2012 · Q15 Marks

The roots of the cubic equation x³ – 7x² + 2x – 3 = 0 are α, β, γ. Find the values of

  1. (i)α² + β² + γ²,[2]
  2. (ii)α³ + β³ + γ³.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.

  1. [B1] States Σα and Σαβ Σα =7 Σαβ = 2
  2. [B1] Uses formula for correctly. Σα² = 7² – 2 × 2 = 45
  3. [M1] Uses formula for Σα³ Σα³ = 7Σα² - 2Σα +9
  4. [A1A1] to obtain result. =315-14+9 = 310

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About this question

Topic
Roots of polynomial equations, A-Level Further Mathematics (syllabus 9231). Structured question, 5 marks.
Source
A-Level Further Mathematics, May/June 2012 Paper 1 Variant 2, question 1.

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