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

1. Jul 19, 2015

### Math Amateur

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 ..

Hope someone can help ... ...

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

Peter

2. Jul 19, 2015

### mathwonk

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?

3. Jul 19, 2015

### Math Amateur

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

Peter

4. Jul 19, 2015

### Math Amateur

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

5. Jul 20, 2015

### micromass

Staff Emeritus
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 $\beta\in F_0$?