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March 28, 2017

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Find the polynomial function P of the lowest possible degree, having real coefficients, with the given zeros.

3+2i, -2 and 1

  • Algebra-zeroes - ,

    The zeroes of polynomials are either real or complex. Complex zeroes always come in with the conjugates.
    Since the three zeroes above do not include conjugates, the minimum degree of polynomial is 3+1=4.

    The polynomial having zeroes of
    3+2i, -2, 1
    and the conjugate 3-2i is therefore
    P(x)=(x-(-2))(x-1)(x-3-2i)(x-3+2i)
    =(x+2)(x-1)(x²-6x+13)
    Expand if necessary

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