IAL 2026 Jan A FP1 Q2 | 國際數學站

Question

[!problem]

In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.

$f(z) = z^4 - 6z^3 + 38z^2 - 94z + 221$

(a) Given that $z = 2 + 3i$ is a root of the equation $f(z) = 0$ , use algebra to find the three other roots of $f(z) = 0$ .

(7)

(b) Show the four roots of $f(z) = 0$ on a single Argand diagram.

(2)

中文翻译

在本题中必须展示所有运算过程。完全依赖计算器技术的解答不可接受。

$f(z) = z^4 - 6z^3 + 38z^2 - 94z + 221$

(a) 已知 $z = 2 + 3i$ 是方程 $f(z) = 0$ 的一个根，用代数方法求 $f(z) = 0$ 的另外三个根。

(7)

(b) 在同一幅 Argand 图上画出 $f(z) = 0$ 的四个根。

(2)