Splitting Fields : Find the splitting fields over Q for x^3+3x^2+3x-4.
Not what you're looking for?
Find the splitting fields over Q for x^3+3x^2+3x-4.
Recall a splitting field is as follows: Let K be a field and let
f(x)=a_0+a_1*x+...+a_n*x^n be a polynomial in K[x] of degree n>0. An extension field F of K is called a splitting field for f(x) over K if there exist elements
r_1,r_2,...,r_n elements of F such that (i) f(x)=a_n(x-r_1)(x-r_2)...(x-r_n) and
(ii) F=K(r_1,r_2,...,r_n).
Purchase this Solution
Solution Summary
Splitting fields are found. The solution is detailed and well presented.
Solution Preview
Please see the attached file for the complete solution.
Thanks for using BrainMass.
Find ...
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.