2013 RI P2 Q4

2013 RI P2 Q4

4 marks

Prelims

If one of the roots of the equation \({{z}^{3}}+2z+k=0\) is \(\mathbf{i}\), find \(k\). Hence find the other two roots.[4]

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Answer:\(k=-\mathbf{i}\) The other roots are \(z=\dfrac{-1+\sqrt5}{2}\mathbf{i}\) and \(z=\dfrac{-1-\sqrt5}{2}\mathbf{i}\)

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