It is given that the roots to the equation $-ix^3 + 5ix^2 + ax + b = 0$, where $a$ and \(b\

Question

It is given that the roots to the equation $-ix^3 + 5ix^2 + ax + b = 0$, where $a$ and $b$ are purely imaginary, are $2+i$, $2-i$ and $1$. Explain why the complex roots occur in conjugate pairs.[2] By using (a) and an appropriate substitution, find the roots of the equation $ix^3 + 5ix^2 + a^*x + b = 0$, where the complex conjugate of $a$ is denoted by $a^*$.[4]

Accepted Answer

(a) After multiplication by $i$, the polynomial has real coefficients, so its non-real roots occur in conjugate pairs (b) $x=-2+i$, $x=-2-i$, or $x=-1$

2025 NYJC P2 Q2

2025 NYJC P2 Q2

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