Question

My math problem is asking me to find all the complex solutions of 3x^2-x+4=0. I recognized this as a quadratic equation but the only thing my problem says is to "find all complex solutions."
I have different answers when I use competing the square or the quadratic equation. Am I not even supposed to use those two methods?
Any help would be greatly appreciated! Math has never been my strong point anyway.

Answer 1

For this you need to use the quadratic formula. So if you use it you will get: \[\frac{ 1\pm \sqrt{-47} }{ 6 }\]

Answer 2

Did you get that?

Answer 3

Hm. I got 1+i(sqrt)47/6

Answer 4

i being a complex number... Gee I must be really off ):

Answer 5

No that is correct.

Answer 6

Oh and the whole thing is divided by 6, not sure how to enter that on openstudy though

Answer 7

I was going to show you the steps after that but you have it already. Okay so they want the complex solutions. So complex solutions include i and square roots. What you have there would be a complex solution.

Answer 8

I'm confused because my problem didnt ask for me to solve it any certain way, just "find all complex solutions".

Answer 9

Are you sure those two roots would be the correct answer?

Answer 10

Do not forget the +/- sign. You should get two answers.

Answer 11

How do I know it shouldnt be solved by completing the square?

Answer 12

Sorry for all the ? :/

Answer 13

When it ask for complex solutions go directly to using the quadratic formula. If you use complete the square or by factoring(if you can) you will get another answer.

Answer 14

Ohhh so the quadratic formula is the "standard" go to in situations like this?

Answer 15

Correct. It will always work in these situations.

Answer 16

Oh wow. Thank you so much for helping me out!

Answer 17

Anytime! Just to clarify the two answers should be \[\frac{ 1+i \sqrt{47} }{ 6 },\frac{ 1-i \sqrt{47} }{ 6 }\]

Answer 18

Okay dokey. Thank you :)

Answer 19

Your welcome :)