rational root theorem

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rational root theorem

[′rash·ən·əl ‚rüt ‚thir·əm]
(mathematics)
The theorem that, if a rational number p / q, where p and q have no common factors, is a root of a polynomial equation with integral coefficients, then the coefficient of the term of highest order is divisible by q and the coefficient of the term of lowest order is divisible by p.
References in periodicals archive ?
In the senior secondary years, when students extend their study to polynomial functions, they come across the rational root theorem (see www.wikipedia.org).
If P is of odd degree, it has a rational root [alpha].
He also proved that the dynatomic curve [[PHI].sub.4,[sigma]](x) = 0 with [sigma](x) = [x.sup.2] + a has no rational points, i.e., [[PHI].sub.4,[sigma]](x) has no rational roots for rational values of a [7].
Yet, her struggle continued, for she was constantly targeted for reasons which had no rational roots and judgment.
If we collocate (24) at the (N) Legendre rational roots of [R.sub.N + 1](t), then we get
He accepted only positive rational roots and ignored all others.
Current research in decision-making has taken a departure from its purely rational roots (Dawes, 1988; Kahneman, Slovic & Tversky, 1982).
Although a lot of people want to pretend that conflict has purely rational roots, the emotional energy tapped by conflict can only be explained by multiple origins.