06 Feb 04
Originally posted by FiathahelQ(sqrt(5)) is all numbers of the form a + b*sqrt(5), where a and b are rationals. Do you mean produce polynomials that have these numbers as roots? Well, p/q + (r/s)*sqrt(5) is a root of the following:
Of course they are algebraic. But the task is to find them.
f(x) = QSX - 2pqSx + (PS - 5RQ) = 0
where P, Q etc mean p^2, q^2 etc.
06 Feb 04
1 edit
Originally posted by AcolyteSorry Acolyte, I forgot something. You were right all of them met the criteria. I forgot to say that the leading coefficient of the polynomial had to be 1.
Q(sqrt(5)) is all numbers of the form a + b*sqrt(5), where a and b are rationals. Do you mean produce polynomials that have these numbers as roots? Well, p/q + (r/s)*sqrt(5) is a root of the following:
f(x) = QSX - 2pqSx + (PS - 5RQ) = 0
where P, Q etc mean p^2, q^2 etc.
So again:
Find all elements in Q(sqrt(5)) which are a root of a polynomial with integer coefficient and leading coefficient 1