If a field K is algebraically closed, then every polynomiel with co efficients in k has a root in K. © Truc. This is an equiral ent way of statling the defiaition of en algebilically closed field. O True. If K is algebraically closed, then every equetion has a solution in K, so every polymomiel hasa root in K. © False. This only applies to non-consbant poly nomiels. A Mome constant poly nomiel such as 1 does not hove a root in K. False, For example, the polynomiel Tk-w +1 does not dEK have a root in k,
If a field K is algebraically closed, then every polynomiel with co efficients in k has a root in K. © Truc. This is an equiral ent way of statling the defiaition of en algebilically closed field. O True. If K is algebraically closed, then every equetion has a solution in K, so every polymomiel hasa root in K. © False. This only applies to non-consbant poly nomiels. A Mome constant poly nomiel such as 1 does not hove a root in K. False, For example, the polynomiel Tk-w +1 does not dEK have a root in k,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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See the pic please (1)
Transcribed Image Text: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 stating the defiaition of
in algebrically closed field,
True. If K is algebraically closed, then every equation has a
solution in K, So every polynomiel haS a root in K.
False. This only applies to non-consbant poly nomiuls. A nonzero
constant polynomiel such as 1 does 2ot hove a root in K.
False, For example, the polymomiel TT k-w) +1 does not
have a root in K,
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