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From: Kent Holing on 1 Apr 2010 05:12 Given any polynomial equation of degree 8 and with rational coefficients. Can anybody provide criteria for the number of classical constructible roots of the given equation? (From Galois theory (group) we can tell when the octicequation is algebraically solvable or not.) Of course, it is simple starting with a quartic eqaution to give examples of equation of degree 8 having either 0 or 8 constructible roots. (An irreducibel quartic with rational coefficients have either 0 or 4 constructible roots. Constructible roots exists if and only if the cubic resolvent of the quartic is reducible (has at leat one rational root).) Best regards, Kent Holing NORWAY
From: What you are reading is Philosophy and P Versus NP. on 1 Apr 2010 09:32 On Apr 1, 6:12 am, Kent Holing <K...(a)statoil.com> wrote: > Given any polynomial equation of degree 8 and with rational coefficients. Can anybody provide criteria for the number of classical constructible roots of the given equation? (From Galois theory (group) we can tell when the octicequation is algebraically solvable or not.) > > Of course, it is simple starting with a quartic eqaution to give examples of equation of degree 8 having either 0 or 8 constructible roots. (An irreducibel quartic with rational coefficients have either 0 or 4 constructible roots. Constructible roots exists if and only if the cubic resolvent of the quartic is reducible (has at leat one rational root).) Results 1 - 10 for polynomial equation of degree 8 and with rational coefficients. Can anybody. (0.22 seconds) Questions on Algebra: Polynomials, rational expressions and ...Questions on Algebra: Polynomials, rational expressions and equations answered by real tutors! ... The problem is a polynominal in x has degree 3. the coefficient of x^2 is 3 less .... (s-6)^3=27(s-8)This question is from textbook Algebra and Trigonometry ... Please can anyone help me with this problem? Thank you. ... www.algebra.com/.../Polynomials...rational.../Polynomials-and-rational-expressions.faq?... Polynomial Of Degree 1 | TutorVista | webFind a 3rd degree polynomial equation with rational coefficients that has ... Question : can anyone help me with this. Answer : because the equation is a ... www.tutorvista.com/ks/polynomial-of-degree-1 UCRY 6(4).pdfby AG Akritas - 1982 - Cited by 2 - Related articles key is "concealed" in a polynomial equation which can be easily exchanged ... Vincent's Theorem Let P(x) = 0 be a polynomial equation of degree a > 1, with rational coefficients and without multiple roots, and let ... which was published in 1836 [8], and it has been used to isolate the real roots of a polynomial ... www.informaworld.com/index/MH116R327R33WJ16.pdf Degree 3 Polynomials | TutorVista | webFind a 3rd degree polynomial equation with rational coefficients that has the roots 3 and ... If anyone can help me out with this I'd appreciate it a lot. ... www.tutorvista.com/ks/degree-3-polynomials Questions on Algebra: Polynomials, rational expressions and ...The equation does not allow two solutions to the problem. ... but I'm not exactly sure which one, and how to. x%5E4-7x%5E2-8 .... Thanks in advance for anyone who can help!! :)This question is from textbook Prentice Hall Algebra 1 ... Question 189753: I have: Polynomial function with a degree 5, rational ... www.algebra.com/.../Polynomials...rational.../Polynomials-and-rational-expressions.faq?... Factoring A 4th Degree Polynomial? | TutorVista | webA polynomial of degree 2 is called a quadratic polynomial. ... you how to solve 3rd and 4th degree polynomial equations using: - common ... zeros (x intercepts) and the sign of the leading coefficient and the . ... I cheated and used my TI-89, and there aren't any rational roots, which makes this one a bad example. ... www.tutorvista.com/ks/factoring-a-4th-degree-polynomial%3F Questions on Algebra: Polynomials, rational expressions and ...Question 219137: Solve the polynomial equation 3x^4 = 81x ... how did my math book get this answer and can anyone explain by defintions ... Question 219501: My math question is as follows: Determine a polynomial P(x) with real coefficients and of degree 5 for which .... Question 220157: How would you do x3-4x2+2x-8 ... www.algebra.com/.../Polynomials...rational.../Polynomials-and-rational-expressions.faq?... Solve This 4th Degree Polynomial? | TutorVista | webA polynomial of degree 2 is called a quadratic polynomial. ... show you how to solve 3rd and 4th degree polynomial equations using: - common factor ... using the zeros (x intercepts) and the sign of the leading coefficient and the . ... 1 litre of water or 8 cups of water per day? does anyone know the title of this ... www.tutorvista.com/ks/solve-this-4th-degree-polynomial%3F Fund theorem of algebraEvery polynomial equation of degree n with complex coefficients has n roots in the ... Then since an arbitrary polynomial can be converted to a monic ... This Euler claimed led to g, h, ... being rational functions of A, B, ..., t. ... proof (although it will come as no surprise to anyone who has studied Cauchy's ... www-history.mcs.st-andrews.ac.uk/.../Fund_theorem_of_algebra.html Learn Online Quintic Polynomial | TutorVista | webQuintic equation - In mathematics, a quintic equation is a polynomial equation of degree five. ... A polynomial of degree 2 is called a quadratic polynomial. ... the discriminant of p(z) is a polynomial in the coefficients a0, a1, ... Add and Subtract polynomials and i can seem to find out how so can anybody help ... www.tutorvista.com/ks/learn-online-quintic-polynomial Support a cure for childhood cancer: Alex's Lemonade ©2009 MeAmI.org "Search for the People!"
From: I.M. Soloveichik on 1 Apr 2010 08:41
> Given any polynomial equation of degree 8 and with > rational coefficients. Can anybody provide criteria > for the number of classical constructible roots of > the given equation? Factor the octic into irreducibles. For those irreducible factors with Galois group of order a power of 2, the roots are constructible. im |