- #1
happyg1
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Homework Statement
Construct a polynomial of degree 7 with rational coefficients whose Galois group over Q is S7
Homework Equations
I need an irreducible polynomial of degree 7 that has exactly 2 nonreal roots.
The Attempt at a Solution
I have just been using trial and error, graphing polynomials of degree 7, making sure that eisenstein's criterion is in force for the irreducible part.
I just change up the coefficients and hope the graph crosses the x-axis 5 times. I'm not having any luck.
Any hints or pointers on how to construct this polynomial?
Thanks,
CC