2023 SJI P2 Q10

2023 SJI P2 Q10

IB Year 5 | Grade 11
12 marks

The roots of a cubic equation form a geometric sequence. The sum of these roots is 0 and the product of these roots is 8.

  1. Find the exact roots of the cubic equation.[7]
  2. Represent the roots by points in an Argand diagram.[2]
  3. Determine, with clear reasons, the type of triangle that is formed by the points in the Argand diagram.[3]

Solution:

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Answer:(a) \(2,-1\pm\sqrt3\mathrm i\) (b) See Argand diagram (c) Equilateral, side \(2\sqrt3\).

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