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For a polynomial f (x) with real coefficients having the given degree and zeros.

Degree 4; zeros 4+2i ; 4 multiplicity 2

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  1. the complex roots occur in conjugate pairs, so 4-2i is also a root. So,
    f(x) = (x-4)^2 (x-(4+2i)) (x-(4-2i))
    = (x-4)^2 ((x-4)-2i)((x-4)+2i)
    = (x-4)^2 ((x-4)^2 - (2i)^2)
    = (x-4)^2 (x^2-8x+16 + 4)
    = (x-4)^2 (x^2-8x+20)

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    oobleck

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