Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
What's rootform? –  joriki Sep 20 '12 at 22:04
@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
If $\alpha,\beta$ are the two roots of $b$, then $$\int_{-m}^m|b(x)|\,\mathrm dx = \int_{-m}^mb(x)\,\mathrm dx-2\int_{\alpha}^\beta b(x)\,\mathrm dx=a(m)-a(-m)-2a(\beta)+2a(\alpha) $$ So the question is whether $a(\alpha)-a(\beta)$ can be expressed by radicals. –  Hagen von Eitzen 10 hours ago

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.