College algebra

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Form a polynomial f(x) with real coefficents having the given degree and zeros degree 5; zeros: 5; -i; -9 +i
f(x)=a

  • College algebra -

    recall that complex roots come in conjugate pairs, so the complete factorization is

    (x-5)(x+i)(x-i)(x-(-9+i))(x-(-9-i))
    (x-5)(x^2+1)((x+9)-i)((x+9)-i)
    (x-5)(x^2+1)((x+9)^2+1)
    (x-5)(x^2+1)(x^2+18x+82)
    x^5+13x^4-7x^3-397x^2-8x-410

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