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Math Help - Need Help with form a polynomial

  1. #1
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    Need Help with form a polynomial

    Form a polynomial F(x) with real coefficients having the given degree and zeros.

    Degree: 3 ; zeros: -2 and 3 + i


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  2. #2
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    Degree 3 = Three zeroes.

    These zeroes (say a, b, and c) are expressed as factors in a polynomial in the form

    f(x) = (x-a)(x-b)(x-c)

    I see you already have two zeroes, and need a third one to complete this polynomial. Since you need a polynomial with real coefficients, you must make sure the imaginary part of the zero (3 + i) is eliminated during the expansion.

    Hint: Any complex zeroes will exist as conjugate pairs in polynomial with real coefficients (conjugate pair theorem).
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