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5 March, 13:55

Find the polynomial equation of least degree with roots - 1, 3, and (+/-) 3i

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  1. 5 March, 14:18
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    Each of these roots can be expressed as a binomial:

    (x+1) = 0, which solves to - 1

    (x-3) = 0, which solves to 3

    (x-3i) = 0 which solves to 3i

    (x+3i) = 0, which solves to - 3i

    There are four roots, so our final equation will have x^4 as the least degree

    Multiply them together. I'll multiply the i binomials first:

    (x-3i) (x+3i) = x²+3ix-3ix-9i²

    x²-9i²

    x²+9 [since i²=-1]

    Now I'll multiply the first two binomials together:

    (x+1) (x-3) = x²-3x+x-3

    x²-2x-3

    Lastly, we'll multiply the two derived terms together:

    (x²+9) (x²-2x-3) [from the binomial, I'll distribute the first term, then the second term, and I'll stack them so we can simply add like terms together]

    x^4 - 2x³-3x²

    +9x²-18x-27

    x^4-2x³+6x²-18x-27
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