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31 January, 02:24

Find the general form of all real polynomials of least degree which have zeros 2 + i and - 1 + 3i

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  1. 31 January, 03:53
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    The coefficients must be real so each complex root must have a conjugate: 2-i and - 1-3i.

    The factorisation is (x-2-i) (x-2+i) (x+1-3i) (x+1+3i) = (x²-4x+5) (x²+2x+10).

    Expanded this is:

    x⁴+2x³+10x²

    -4x³-8x²-40x

    +5x²+10x+50=

    x⁴-2x³+7x²-30x+50.
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