Question

Help me find complex zeros of x^2+2x+2

Answer 1

I'm sure there are different methods, but can I use the quadratic formula?

Answer 2

yes. or completing the square

Answer 3

Can we work it both ways so I can be comfortable?

Answer 4

That is where I am at for q formula.

Answer 5

I figured it out on my own! YAY!

Answer 6

ya

your polynomial is ax^2 + bx + c

quadratic:
\[x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a } = \frac{ -2 \pm \sqrt{4 - 8} }{ 2 } = -1 \pm i\]
completing square:
consider only x^2 + bx:
\[x^2 + bx = (x+\frac{ b }{ 2 })^2 - \left( \frac{ b }{ 2 } \right)^2\]

\[x^2 + 2x + 2 =\left[ (x+1)^2 - 1 \right] + 2 = (x+1)^2 + 1\]

finding roots of: (x+1)^2 + 1 = 0:
\[(x+1)^2 = -1\]\[x+1 = \pm \sqrt{-1}\]\[x = -1 \pm \sqrt{-1} = -1 \pm i\]

i just saw your quadratic. looks good. do you know how to simplify it into what i got?

Answer 7

looks good. u got it. ignore last part lol. didnt scroll back before typing

Answer 8

THANK YOU!

Answer 9

Thanks for all you did, typing that out is a lot of work! I used my iPad and air server. lol

Answer 10

hehe cool :) np