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Let $a(x)$ and $b(x)$ be integer irreducible polynomials where $b$ is U-shaped in the interval mentioned below and has 2 distinct real zeros. The zeros of $b$ cannot be expressed by radicals. Also $b$ is the derivative of $a$ and $b$ has degree prime of type 7 mod 8.

Is it possible that there exists a nonzero integer $m$ such that the interval $[-m,m]$ contains the two zeros of $b$ and the integral from $-m$ to $m$ of the absolute value of $b(x)$ $dx$ can be given in rootform?

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What's rootform? –  joriki Sep 20 '12 at 22:04
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@joriki : wild guess would be "expressible by radicals"? But it deserves clarification... –  Patrick Da Silva Sep 20 '12 at 22:22
    
If $b$ has odd degree, its graph can't be U-shaped. –  Gerry Myerson Sep 21 '12 at 0:20
    
Ah sorry , i mean U shaped in the interval. –  mick Sep 21 '12 at 13:41
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mick, if you want to be sure I see a reply, you have to write @Gerry. –  Gerry Myerson Sep 23 '12 at 12:57

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