Question

can someone explain to me how you know when you need to put and i (imaginary) into your answer when you are solving symbolically in standard form.
ex: x^2+9=0

Answer 1

Sure, I can assist.

Answer 2

When you use the quadratic equation, and you get a negative number inside of the determinant (the part that has the square root), you will need to use an i

Answer 3

i is just a way for math people to deal with a negative number inside of a square root
i = sqrt(-1)

Answer 4

Does that make sense? Or would like an example answer?

Answer 5

that really does help a lot. could you give me an example though?

Answer 6

Of course.
Let's use your x^2 + 9 example

Answer 7

so sqrt(-16) = sqrt(16)(sqrt(-1) = 4i

Answer 8

First, I need to know two things:
Do you know how to use the quadratic formula?

Answer 9

yes i do

Answer 10

Awesome!
So what is A,B and C in x^2 + 9?

Answer 11

okay so i'm a little confused since there are only two sets. i know i probably sound really dumb!

Answer 12

Nah... don't worry about it! We all have to start somewhere! I prefer to explain slowly and take the long way to the answer as opposed to just saying what the answer is. So this is perfect.

Answer 13

We can agree that A, B and C are normally used this way:

Ax^2 + Bx + C

Right?

Answer 14

haha that's exactly what i need, so thank you (:

Answer 15

yeah that makes sense

Answer 16

Alright! So our problem is:

X^2 + 9

Answer 17

Pick any of the letters that you already know. (Hint: I think you know what C is)

Answer 18

c=9?

Answer 19

Perfect! C is always the number without the X.

Answer 20

sweet. so is a=x^2?

Answer 21

perfect!

Answer 22

So this leaves us with a mysterious B that we can't see.

I'll give you a hint: B technically exists. But we just ignore it. So what is B most likely? In other words, how many X's do we have (note that we don't care about X^2. Just X by itself).

Answer 23

Oh wait... I said something wrong. I meant to say "A is linked to x^2" I'll explain that some more in a moment.

Answer 24

is it 0?

Answer 25

perfect!

Answer 26

Ok, earlier I meant to say that A doesn't equal X^2, but rather, that it is related to x^2.

How many X^2 do we have in x^2 + 9?

Answer 27

1

Answer 28

bingo!

Answer 29

So, our formula, when expanded, is actually:

1x^2 + 0x + 9

Answer 30

Does this make sense? If not, do ask.

Answer 31

yes it does completely

Answer 32

Awesome! Just to make sure: could you tell me A,B,C in:

3x^2 - 4x ?

Answer 33

a=3
b=0
c=4

Answer 34

Close. But remember: C is always the number by itself, and B is always next to the X.

So it's Ax^2 + Bx + C

Answer 35

So try that question again.
3x^2 - 4x

Answer 36

right so a=3
b=4
and c=0

Answer 37

Close again. You forgot a sign. ;)

Answer 38

ahhh -4

Answer 39

Yup!

Answer 40

Alright, so I think you've got the letters down. Now let's go back to your original question:

x^2 + 9

Remind me of our A,B,C on this question.

Answer 41

okay
a=1
b=0
c=9

Answer 42

Perfect!

Now, do you remember the quadratic equation? Could you post it for me?

Answer 43

b^2 +/- square root4ac/2a

Answer 44

4ab

Answer 45

Actually it's

-b + or - the square root of b^2 - 4ac, all divided by 2a

Answer 46

Do you remember this one?

Answer 47

yeah kinda, i just don't have the best memory

Answer 48

it's in my notes though

Answer 49

Has your teacher told you about the "pop goes the weasel" song to remember it?

Answer 50

Also known as the "jack in the box" song?

Answer 51

haha no

Answer 52

Ah. Do you know how the real pop goes the weasel song sounds?

Answer 53

yeah

Answer 54

Awesome. Just sing this a few times and you'll never forget it again:

Negative B.. plus or minus the squareee root of B squared... minus four a c, allll over twoooo a.

(like the pop goes the weasel song) :P

Answer 55

ANYHOW.....

Answer 56

haha cool, thanks

Answer 57

-b + - squareroot (b^2 - 4ac)
--------------------------
2a

Answer 58

Alright, so we know that our A is 1 and our B is 0 (yay!) and our C is 9

Answer 59

0 + - square root (0 - 4*1*9)
---------------------------
2*1

Answer 60

Does this make sense so far?

Answer 61

yes

Answer 62

awesome. Do you recall what the + - means?

Answer 63

that's where the i comes in, right?

Answer 64

not really
It just means "find the answer you get when you add 0 and the stuff in the square root, and then do it again by subtracting the stuff in the square root"

Answer 65

oh okay

Answer 66

Before we finish up the harder i question, let me show you an easy question:

If we were at this point:

9 +- squareroot(25)
-------------------
2*1

Could you tell me what our two answers would be?

Hint: square roots are technically exponents, so remember the rules of PEMDAS. Tell me if you haven't been taught PEMDAS/Order of operations.

Answer 67

7 and 2

Answer 68

Perfect!

Answer 69

(:

Answer 70

Now, here's an i example:

what is the square root of negative 25?

Answer 71

5i

Answer 72

perfecto!

Answer 73

And if I told you something like:

0 +- squareroot(-36) ?

Answer 74

6i and -6i?

Answer 75

Bingo!
And if I asked you to divide both answers by 2?

Answer 76

3i and -3i?

Answer 77

You got it, buddy!

Now let's do a 'totally different' problem.

0 + - square root (0 - 4*1*9)
---------------------------
2*1


This was what we had left after putting in our a,b,c values. Go ahead and finish it up for me.

Answer 78

is it 3i and -3i again?

Answer 79

Yep! Sneaky, aren't I? ;)

Answer 80

haha (:

Answer 81

And that's your answer to x^2 + 9!

The reason it doesn't have any 'real' answers is because it never touches the X axis (which would USUALLY be the real answer).

Answer 82

okay, that makes sense. thank you so much for your help, i really appreciate it!!

Answer 83

No problemo!
Would you like to take this one step further and learn WHY that's the answer?

Answer 84

i would love that, but i have my exam in the morning so i should probably get some sleep, but thank you!

Answer 85

Haha ok. Good night, then! Feel free to subscribe to me so that you can ask me questions if you have any in the future. Best of luck!

Answer 86

i will, thank you, i'm going to need it!

Answer 87

Awesome job uber.

Answer 88

Thanks polpak, I appreciate it!