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Math Help - Roots related question

  1. #1
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    Roots related question

    Hey guys I was having trouble with this question can someone plesase explain it to me in detail. thanks much appreciated.
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  2. #2
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    Quote Originally Posted by ballaholic8 View Post
    Hey guys I was having trouble with this question can someone plesase explain it to me in detail. thanks much appreciated.
    x^3 - 3^3 = (x - 3)(x^2 + 3x + 9).

    Therefore the roots of x^3 - 27 are x = 3 and the solutions to x^2 + 3x + 9 = 0.

    -----------------------------------------------------------------------------------------------------------------

    A polynomial with roots x = 3 \pm i and x = -4 is

    a (x - [-4])(x - [3 + i])(x - [3 - i]) = a (x + 4)([x - 3] - i)([x - 3] + i) = a (x + 4)([x - 3]^2 + 1) = a(x + 4)(x^2 - 6x + 10)

    where a is any real number except zero.
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