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third degree with zeros of 2-i,2+i and 2 and a leading coefficient of 4. Construct a polynomial function with stated properties

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grace

  1. let's start with the two complex zeros
    sum of roots = 2-i + 2+i = 4
    product of roots = (2-i)(2+i) = 4 - i^2 = 5
    so the quadratic that would form those two zeros is
    x^2 - 4x + 5

    your function will be
    f(x) = 4(x - 2)(x^2 - 4x + 5)

    expand and simplify if you have to.

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    Reiny

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