Explore BrainMass
Share

contrapositive

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Let K be a field and let f(x) in K[X] be a polynomial whose degree is either 2 or 3. Show that f(x) is irreducible if and only if it has no roots.

© BrainMass Inc. brainmass.com March 21, 2019, 10:52 pm ad1c9bdddf
https://brainmass.com/math/linear-algebra/proving-function-irreducible-435431

Solution Preview

Let K be a field and let f(x) in K[X] be a polynomial whose degree is either 2 or 3. Show that f(x) is irreducible if and only if it has no roots in K.

Proof: Let K be a field and let f(x) in K[X] be a polynomial whose degree is either 2 or 3.
(=>) Suppose f(x) is reducible in K[x]. Then there exist non-constant ...

Solution Summary

This solution shows how to solve a linear algebra problem.

$2.19