- #1
Niall101
- 20
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IS f(x)= x^4 + x^3 -x^2 - 2x -2 irreducable over Q??
IS f(x)= x^4 + x^3 -x^2 - 2x -2 irreducable over Q??
Attempt:
Ive shown that this has no linear factors as +-1 +-2 are not roots.
Then I let F(x)=(x^2+ax+b)(x^2+cx+d)
And I end up with
a +c=1
d+ac+b=-1
ad+bc=-2
bd=-2
But i can seam to show why no a b c d exist (or Exist)
Is there an easier approach?
I have an exam in 12 hours so I hope soeone can help!
Thanks in advance!
Niall
IS f(x)= x^4 + x^3 -x^2 - 2x -2 irreducable over Q??
Attempt:
Ive shown that this has no linear factors as +-1 +-2 are not roots.
Then I let F(x)=(x^2+ax+b)(x^2+cx+d)
And I end up with
a +c=1
d+ac+b=-1
ad+bc=-2
bd=-2
But i can seam to show why no a b c d exist (or Exist)
Is there an easier approach?
I have an exam in 12 hours so I hope soeone can help!
Thanks in advance!
Niall