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College Algebra! help!

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Form a polynomial f(x) with the real coefficients having the given degree and zeros.
Degree 5; Zeros: -4; -i; -2+i

f(x)=a( )

  • College Algebra! help! -

    complex zeros always come in conjugate pairs
    so if -i is a zero , so is +i
    if -2+i is a zero, so is -2 - i
    the zero of -4 comes from the factor (x+4)
    the zeros of ±i come from (x^ + 1)

    the zeros of -2 ± i produce
    (x-(-2+i))(x - (-2-i) )
    = (x^2 + 4x + 5)

    so a possible polynomial is
    f(x) = (x+4)(x^2 + 1)(x^2 + 4x + 5)

    expand if needed

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