(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Construct a polynomial of degree 7 with rational coefficients whose Galois group over Q is S7

2. Relevant equations

I need an irreducible polynomial of degree 7 that has exactly 2 nonreal roots.

3. 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

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# Galois groups over the rationals

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