2. Let K be an extension of F and let a e K be algebraic over F. Then (i) There exists a unique monic irreducible polynomial p (x) e F (x] of least positive degree such that p (a) = 0. (ii) If g (x) e F[x] is such that g (a) = 0, then p (x) divides g (x).

2. Let K be an extension of F and let a e K be algebraic over F. Then (i) There exists a unique monic irreducible polynomial p (x) e F (x] of least positive degree such that p (a) = 0. (ii) If g (x) e F[x] is such that g (a) = 0, then p (x) divides g (x).

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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2. Let K be an extension of F and let a e K be algebraic
over F. Then
(i) There exists a unique monic irreducible polynomial
p (x) e F (x] of least positive degree such that p (a) = 0.
(ii) If g (x) e F[x] is such that g (a) = 0, then p (x) divides g (x).

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