Question

State how many imaginary and real zeros the function has.

f(x) = x^4 + 12 x^3 + 37x^2 + 12x + 36

Answer 1

2 imaginary 2 real

Answer 2

If you want confirmation on your answer, perhaps you could either say what the zeroes are or show a little bit of the work you went through to get your answer.

Answer 3

because they are only two real numbers

Answer 4

The rule of signs will admit to possibly either 4 or 2 or no negative reals zeros. The same rule of signs shows no positive reals. So, the reals zeros still could be 4, or 2, or none. How is it you come up with two reals?

Answer 5

I'm not implying either that you are wrong or that you are right at this point. But I'm sure you didn't grab a number out of the air.

Answer 6

i saw 2 because i see only 2 imaginary and real i guess i might be wrong

Answer 7

i know that are only 0 or 2 and 4

Answer 8

idk now ur making me questioning my anserw

Answer 9

Well, again, I'm not saying yet whether you are right or wrong. I'm saying that I don't see any evidence of how you got your answer yet. I want to help you, but I can't just give out an answer. It's good to question your answer. It helps anyone think things out, and in the end, you will know things better and clearer. One way to know if there are 2 reals and two imaginaries is to find the zeros.

Answer 10

I took your problem and did a quick synthetic division and cam up with what is the right answer. If you could show me something, I can help you better, and I want to be able to do that for you.

Answer 11

ohh ok let me show u if u want me to

Answer 12

It's only for your benefit.

Answer 13

ok np

Answer 14

1 real 3 imaginary i just watched the video on it again an since the there are 1 number by them selvees and 3 i

Answer 15

Actually, you were right the first time in that there are 2 real zeros and 2 imaginary zeros. But it looks like you are guessing and are not sure how to do another problem that would be similar. I could show you a methodology and then you would be able to perform any such problem on your own. Wouldn't that be best?

Answer 16

yes please

Answer 17

Ok, I'm going to make a drawing of how I performed the synthetic division. But first, to recap where we are up to this point, we know that there are no positive reals zeros because there is no sign change going from term to term. If we put in a negative, we will see 4 sign changes, so we know that there are either 4 or 2 or 0 negative reals. We also know that the reals will be factors of 36 over factors of 1, but since they will all be negative from the law of signs, we can look at just the negative factors.

Answer 18

ok so those are pretty much the rules

Answer 19

So, there is -6 as a zero TWICE, and then you are left with x^2 + 1, which gives +-i.

Answer 20

Are you familiar with synthetic division?

Answer 21

then i go with -6 again

Answer 22

yuppp

Answer 23

So, the zeros are -6, -6, i, -i.

Answer 24

so two real two negative i kinda did it through watching a video and applying it

Answer 25

Which is 2 reals and 2 imaginaries. But you would have to do something similar to what I did or you wouldn't really get an answer. Perhaps the video showed you some shortcuts, which is OK if all you want to do is know the number of reals without knowing the values. That's OK. I haven't seen the video so I can't critique it.

Answer 26

ya it was a shortcut but thank you so much !

Answer 27

It was nice working with you and good luck on all your studies.