write, in extended form, a polynomial(with real coefficients) of degree 3, with solutions 2,2-i.

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  1. complex roots always come in pairs, so if 2-i is a root, so is 2+i
    using the sum and product of roots property of a quadratic,
    sum of roots = 2-1 + 2+i = 4
    product or roots = (2-i)(2+i) = 4 - i^2 = 5
    so the quadratic part would be
    x^2 - 4x + 5
    the other factor would be x-2

    so the polynomial is
    (x-2)(x^2 - 4x + 5)

    I will leave it up to you to expand it, if you need it in that form.

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