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Math Help - How do I find the complex roots using the quadratic forumula for 4th degree poly?

  1. #1
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    How do I find the complex roots using the quadratic forumula for 4th degree poly?

    For: z^4 + 7z^2 +2

    how can I use the quadratic formula to find the complex roots?

    I tried substituting  u = z^2, but when I use the quadratic formula I get real answers and don't know where to substitute u back in.

    I also tried thinking of the values for a b and c as z^2, 7 and 2, but I cam across difficulties when trying to simplify the contents of the square root.
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  2. #2
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    Re: How do I find the complex roots using the quadratic forumula for 4th degree poly?

    Quote Originally Posted by terrorsquid View Post
    For: z^4 + 7z^2 +2

    how can I use the quadratic formula to find the complex roots?

    I tried substituting  u = z^2, but when I use the quadratic formula I get real answers and don't know where to substitute u back in.

    I also tried thinking of the values for a b and c as z^2, 7 and 2, but I cam across difficulties when trying to simplify the contents of the square root.
    z^2=t

    t^2+7t+2=0 \Rightarrow t_1=-0.2984~,~t_2=-6.7016

    z^2=-0.2984 \Rightarrow z_{1,2}=\pm \sqrt {0.2984} \cdot i

    z^2=-6.7016 \Rightarrow z_{3,4}=\pm \sqrt {6.7016} \cdot i
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