the polynomial x^4+8x+12=0 has the Galois group A4. I have all its roots, but can't figure out its splitting field. The roots are(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\alpha_1=\sqrt{2}(\sqrt{\cos{(\pi/9)}}+i\sqrt{\cos{(2\pi/9)}}+i\sqrt{\cos{(4\pi/9)}})[/tex]

[tex]\alpha_2=\sqrt{2}(\sqrt{\cos{(\pi/9)}} - i\sqrt{\cos{(2\pi/9)}}-i\sqrt{\cos{(4\pi/9)}})[/tex]

[tex]\alpha_3=\sqrt{2}(-\sqrt{\cos{(\pi/9)}} + i\sqrt{\cos{(2\pi/9)}}-i\sqrt{\cos{(4\pi/9)}})[/tex]

[tex]\alpha_4=\sqrt{2}(-\sqrt{\cos{(\pi/9)}} - i\sqrt{\cos{(2\pi/9)}}+i\sqrt{\cos{(4\pi/9)}})[/tex]

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Splitting field with Galios group A4

Loading...

Similar Threads for Splitting field Galios | Date |
---|---|

I Splitting Fields: Anderson and Feil, Theorem 45.6 ... | Jun 23, 2017 |

I Splitting Fields: Anderson and Feil, Theorem 45.5 ... | Jun 22, 2017 |

I Splitting Fields: Anderson and Feil, Theorem 45.4 ... | Jun 21, 2017 |

I Splitting Fields and Separable Polynomials ... | May 31, 2017 |

I Splitting Fields - Example 3 - D&F Section 13.4, pages 537 - | May 14, 2017 |

**Physics Forums - The Fusion of Science and Community**