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

• Mar 4th 2012, 06:37 PM
terrorsquid
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.
• Mar 5th 2012, 12:41 AM
princeps
Re: How do I find the complex roots using the quadratic forumula for 4th degree poly?
Quote:

Originally Posted by terrorsquid
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.

$z^2=t$

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

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

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