# A multiple choice question on field extensions [closed]

Which of the following statement(s) is / are true?
1. $\mathbb{C} (x)$ is algebraically closed, where $x$ is an indeterminate.
2. An algebraically closed field must be of characteristic $0$.
3. If $E$ is an algebraically closed extension field of $F$, then $E$ is an algebraic extension of $F$.

can anyone help me to solve this problem.thanks for your time.

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## closed as off-topic by Bookend, Eric Wofsey, Zachary Selk, S.Panja-1729, Ivo TerekOct 11 '15 at 2:35

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Bookend, Eric Wofsey, Zachary Selk, S.Panja-1729, Ivo Terek
If this question can be reworded to fit the rules in the help center, please edit the question.

1. The question is whether all polynomials with coefficients in $\mathbf C(x)$ have a root. Hint: consider $f(T) = T^2-x$. In other words, does $x$ have a square root in $\mathbf C(x)$?
2. That's a bit weird; why would that be true? Anyway, if you are familiar with the fact that every field has an algebraic closure, look at the algebraic closure of $\mathbf F_2$. What can you say about its characteristic?
3. What do you think of $\mathbf C$ over $\mathbf Q$?