2024 IGCSE Additional Mathematics October/November 0606/22 Q3

2024 IGCSE Additional Mathematics October/November 0606/22 Q3

5 marks

DO NOT USE A CALCULATOR IN THIS QUESTION.

The polynomial \(\mathrm{p}\) is defined by \(\mathrm{p}(x)=ax^3-3x^2-3x+b\), where \(a\) and \(b\) are constants.

  1. Given that \(x=2\) and \(x=-1\) are roots of the equation \(\mathrm{p}(x)=0\), find \(a\) and \(b\).[3]
  2. Solve the equation \(\mathrm{p}(x)=0\).[2]

Solution:

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Answer:(a) \(a=b=2\). (b) \(x=-1,\dfrac12,2\).

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