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college algebra

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

degree 5; zeros 5; -i; -6+-i

f(x)= a(?)

Please show step by step work.

  • college algebra -

    since complex roots come in pairs, the factors are

    (x-5)(x-i)(x+i)(x-(-6+i))(x-(-6-i))
    (x-5)(x-i)(x+i)((x-6)-i)((x-6)+i)
    (x-5)(x^2+1)(x^2+12x+37)

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