(New page: Question states: Find the splitting field of x^4 + x^2 + 1 = (x^2 + x + 1)(x^2 - x + 1 ) over Q Hint: Use the quadratic formula to find the roots (r1,r2,r3,r4) of the quadratics. The roo...) |
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| + | Can you give an example of this manipulation? Also, The root is a+bi but the answer is <math>Q(\sqrt -3)</math>, so I am confused. | ||
Latest revision as of 21:28, 19 November 2008
Question states: Find the splitting field of x^4 + x^2 + 1 = (x^2 + x + 1)(x^2 - x + 1 ) over Q
Hint: Use the quadratic formula to find the roots (r1,r2,r3,r4) of the quadratics. The roots are in the form a + bi and then you can show manipulating r1 you can get r2,r3,r4 so therefore r1 is a splitting field.
--Robertsr 23:32, 18 November 2008 (UTC)
Can you give an example of this manipulation? Also, The root is a+bi but the answer is $ Q(\sqrt -3) $, so I am confused.
