Do not use a calculator in answering this question. It is given that $2-\mathbf{i}$ is a root of the

Question

Do not use a calculator in answering this question. It is given that $2-\mathbf{i}$ is a root of the equation $2{{z}^{3}}+a{{z}^{2}}-2z+b=0$. Find the values of the real numbers $a$ and $b$ and the remaining roots of the equation. [4] Using these values of $a$ and $b$, deduce the roots of the equation $b{{z}^{3}}-2{{z}^{2}}+az+2=0$. [2]

Accepted Answer

(a) $a=-5$, $b=15$, remaining roots $2+\mathrm{i}$ and $-\dfrac32$ (b) $z=-\dfrac23$, $z=\dfrac25\pm\dfrac15\mathrm{i}$

2022 YIJC P1 Q1

2022 YIJC P1 Q1

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