Do not use a calculator in answering this question. The equation $2{{z}^{3}}+5{{z}^{2}}+pz+q=0$ has

Question

Do not use a calculator in answering this question. The equation $2{{z}^{3}}+5{{z}^{2}}+pz+q=0$ has a root $z=-1-\mathrm{i}$, where $p$ and $q$ are real constants. Find $p$ and $q$ and all the roots of the equation. [7]

Accepted Answer

$p = 6$, $q = 2$; Roots: $-\displaystyle\frac{1}{2}$, $-1+\mathrm{i}$, $-1-\mathrm{i}$

2020 CJC P1 Q3

2020 CJC P1 Q3

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