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March 25, 2017

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write a polynomial function f of least degree that has the rational coefficients, a leading coefficient of 1, and the given zeros. Given zeros: -2,2,-1,3, sqrt 11

  • pre-ap Algebra 2 - ,

    (x+2)(x-2)(x+1)(x-3) takes care of the integer roots.

    Now, if √11 is a root, then (x-√11) is a factor, but that leaves a dangling √11, which will show up in the coefficients. So, you also need to include (x+√11), since

    (x-√11)(x+√11) = x^2-121, which has rational coefficients.

    So, the final polynomial is

    f(x) = (x+2)(x-2)(x+1)(x-3)(x-√11)(x+√11)

    and yu can expand that out if you like.

  • pre-ap Algebra 2 - ,

    oops. (x-√11)(x+√11) = x^2-11

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