If a field K is algebraically closed, then every polymomiel with co- efficients in k has a root in K. © True. This is an equiral ent way of statling the defiaition of in algebiuically closed field. O True. If K is algebraically closed, theen every equation hos a solution in K, so eve ry polymomiel has a root in K. O False. This only applies to non-consbant poly nomicls. A nonzeu constant polynomiel such as 1 does not hove a root in K. O False. For example, the polynomisl T k-W +1 does not dEK have a root in K,

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A:

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.