Question

97

Answer 1

This one there are a few ways to do this.
One way is the use the quadratic formula:
\[x = \frac{ 6\pm i \sqrt{4(1)(58)-(-6)^{2}}}{ 2 } = \frac{ 6\pm i \sqrt{196} }{ 2 } = 3\pm7i\]

The other way is to compare roots.
Sum of roots should add to -b/a = 6
and product should give c/a = 58. Only a satisfies this criteria.

Answer 2

when i squared rooted the 196 i get 14 but i got the sane answer as you. thanks for the help!

Answer 3

I divided the 14 by 2 in one step. Yep no worries. The roots method may be easier in some circumstances. Also there is the theorem that if one complex number is a root, then its conjugate must also be a root (for a real coefficient polynomial). So you could plug one of the possible roots into the poly and if it gives 0, you automatically know its conjugate is a root.