# Affine Algebraic Curves - Kunz - Exercise 1 - Chapter 1

Gold Member
I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves"

I need help with Exercise 1, Chapter 1 ...

Indeed ... I am a bit overwhelmed by this problem ..

Exercise 1 reads as follows:

Hope someone can help ... ...

To give a feel for the context and notation I am providing the start to Chapter 1, as follows:

Peter

## Answers and Replies

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mathwonk
Homework Helper
suppose you have a polynomial of degree d over F and d-1 roots are in F. Can you conclude that the last root is also in F?

Gold Member
Sorry mathwonk ... not sure ... can you help further ...

Peter

Gold Member
Well ... maybe if F is an algebraically closed field, then all the d roots of the polynomial would be in F ...

Is that correct?

Peter

Well ... maybe if F is an algebraically closed field, then all the d roots of the polynomial would be in F ...

Is that correct?

Peter
You don't want them to be in ##F##, you want them to be in ##F_0##. Think about mathwonk's hint. If ##(X-\alpha)(X-\beta)## is a polynomial in ##F_0## such that ##\alpha\in F_0##, why is ##\beta\in F_0##?