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A-LevelMathematicsComplex numbers9709/31 · Oct/Nov 2020 · Q77 Marks

Verify that –1 + √5i is a root of the equation 2x³ + x² + 6x – 18 = 0.

  1. (a)Verify that –1 + √5i is a root of the equation 2x³ + x² + 6x – 18 = 0.[3]
  2. (b)Find the other roots of this equation.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

  1. Substitute -1 + √5 i in the equation and attempt expansions of x² and x³
  2. Use i² = -1 correctly at least once
  3. Complete the verification correctly
  4. State second root -1-√5i
  5. Carry out a complete method for finding a quadratic factor with zeros −1+√5i and -1-√5i
  6. Obtain x² + 2x + 6
  7. Obtain root x = 3/2

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About this question

Topic
Complex numbers, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Oct/Nov 2020 Paper 3 Variant 1, question 7.

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