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Math Help - complex conjugate roots

  1. #1
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    complex conjugate roots

    I have the following problem which i hope someone can point me in the right direction of solving:

    The equation X^4+40x+39 has 4 roots, if two of the roots are the complex conjugate roots 2+J3 and 2-J3 by a process of long divison and slving a quadratic equation find the other two roots.

    The exaple I am given in the book i have gives you the real roots to start with but gives no example of an equation that gives you the imaginary roots. I am looking for somehelp with how to get started on this one.

    Any help is apprecciated
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  2. #2
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    Hello,

    2 \pm 3j is a root.
    Therefore the polynomial can be factored by [x-(2+3j)][x-(2-3j)]=[(x-2)-3j][(x-2)+3j]

    We know that (a-b)(a+b)=a^2-b^2.

    So the previous line equals to :

    =(x-2)^2-(3j)^2=x^2-4x+4-9\underbrace{j^2}_{-1}=x^2-4x+13

    Now, you can try the division process...
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  3. #3
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    Quote Originally Posted by ally79 View Post
    I have the following problem which i hope someone can point me in the right direction of solving:

    The equation X^4+40x+39 has 4 roots, if two of the roots are the complex conjugate roots 2+J3 and 2-J3 by a process of long divison and slving a quadratic equation find the other two roots.

    The exaple I am given in the book i have gives you the real roots to start with but gives no example of an equation that gives you the imaginary roots. I am looking for somehelp with how to get started on this one.

    Any help is apprecciated
    Note: Only one of the roots needed to be given since all coefficients of the quartic are real and so the conjugate root theorem could be used to get the other.
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