Question

Suppose that a polynomial function of degree 5 with rational coefficients has the given numbers as zeros. Find the other zero( s):

-1, radical 3, 11/3

Answer 1

(x+1)(x-√3)(x+√3)(3x-11)

no way to tell the 5th root.

Answer 2

One of the rational roots would have to be a double root, so it could be

y = (x+1)^2(x-√3)(x+√3)(3x-11) = (x+1)^2(x^2+9)(3x-11)
or
y = (x+1)(x-√3)(x+√3)(3x-11)^2 = (x+1)(x^2+9)(3x-11)^2

Answer 3

did I miss an i somewhere?
(x-√3)(x+√3) = x^2-3

Answer 4

Suppose that a polynomial function of degree 5 with rational coefficients has -2, 5, and 3 - I as zeros. Find the other zeros.