Polynomial ring/Ordered field/Ordered quotient field/Not archimedean/Exercise

Let ${}K$ be an ordered field, let ${}K[X]$ be the polynomial ring over ${}K$ and set

${}Q=K(X)\,,$

the field of rational functions over ${}K$. Show, using exercise, that ${}Q$ can be made into an ordered field, which is not an archimedean ordered field.

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