2013 TPJC P2 Q3
2013 TPJC P2 Q3
6 marks
Prelims
Do not use a graphing calculator in answering this question.
- Given that \(w=\mathrm{ }1\mathrm{ }+\mathrm{ }\mathbf{i}\) is a root of the equation\({{w}^{3}}+\mathrm{ }3{{w}^{2}}+pw+q=\mathrm{ }0\),find the values of the real numbers \(p\) and \(q\).[4]
- For these values of \(p\) and \(q\), solve the equation in part (i).[2]
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Answer:\(\text{(b)(i)}\ p=-8,\ q=10\) \(\text{(b)(ii)}\ w=-5,\ 1+\mathbf{i},\ 1-\mathbf{i}\)
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