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

For: $\displaystyle z^4 + 7z^2 +2$

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

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

Re: How do I find the complex roots using the quadratic forumula for 4th degree poly?

Quote:

Originally Posted by

**terrorsquid** For: $\displaystyle z^4 + 7z^2 +2$

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

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

$\displaystyle z^2=t$

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

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

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