 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-1/18g/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

f \in K [X]

is an extension

L / K

in which

f (X) = c \prod_{r = 1}^{d} (X - α_{r})

α_{r} \in L

, and which is generated by those roots:

L = K (α_{1}, \dots, α_{d}) .

The generation condition is the required minimality: no proper intermediate field containing

K

can still contain every root.

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