PreCalculus

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

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  1. (x+1)(x-√3)(x+√3)(3x-11)

    no way to tell the 5th root.

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  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

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

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

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