Question

Here @terenzreignz

Answer 1

Where?

Answer 2

You two are up early, aren't you? lawlerz :3

Answer 3

I'm actually still asleep, Renz. That's how awesome I am, I teach maths in my sleep ...
:P

Answer 4

Yeah I ditch him last night TJ

Answer 5

Hmmn... this never gets old...

Answer 6

Why am I not surprised? haha

Answer 7

I know...

Answer 8

Hey Renz, think you can handle this? :D

Answer 9

Haha

Answer 10

Well, seeing as it's daytime, I doubt Josh's gonna fall drowsy again XD
Let's get cracking

Answer 11

Of course I wont.....

Answer 12

You better not ...
\[\large 4z^6-20z^5+35z^4-31z^3=9z^2 - 9z\]

Answer 13

Okay... bring every term to one side of the equation. :)

Answer 14

Hey TJ... gonna buy yourself a new iPhone? ;)

Answer 15

The other side?

Answer 16

I... don't know. Cripes, sometimes I forget how unbelievably loaded you are, Rain :3

Answer 17

The left side, preferably, @EngrChong :)

Answer 18

Transpose, Josh.
So that you have zero on the right side.

Answer 19

Ok....

Answer 20

You should have something like this:
\[\large 4z^6-20z^5+35z^4-31z^3-9z^2 + 9z=0\]

Answer 21

Two of you are tutoring me right now?haha

Answer 22

Well, I can't just sit here and watch, now, can I? XD

Answer 23

Besides, I'm awesomer than him >:)

Answer 24

Of course......XD

Answer 25

Yeah, right, Kurt, even your username says I reign :P

Answer 26

Here we go again hahaah

Answer 27

Anyway, do you get that last part?

Answer 28

Yup..........What's next?

Answer 29

We factor out a z.

Answer 30

\[\large z(4z^5-20z^4+35z^3-31z^2-9z + 9)=0\]

Answer 31

ok

Answer 32

got it....

Answer 33

Okay, so this tells you that 0 is a root, right?

Answer 34

I mean, if z is zero, then
\[\large \color{green}z(4z^5-20z^4+35z^3-31z^2-9z + 9)=0\] will be zero, meaning it won't even matter what THIS\[\large z\color{green}{(4z^5-20z^4+35z^3-31z^2-9z + 9)}=0\] part is.

Answer 35

Yes....

Answer 36

So, let's add that to our list of roots.
By the way, how many roots at most could this equation have?

Answer 37

Roots?

Answer 38

Roots. Solutions. Values of z. Call it what you like, but how many roots could this equation at most possibly have?

Answer 39

6?

Answer 40

That's right. How did you know?

Answer 41

I just counted the 6 of them there

Answer 42

LOL You looked at the answers. Don't. The way to tell how many distinct roots a polynomial equation could have is to look at its highest exponent, which, by the way, was 6, remember? :D

Answer 43

No i didnt...

Answer 44

Then what did you count?

Answer 45

I counted 4z^5 -20z^4

Answer 46

etc

Answer 47

That's the wrong idea. Stick to the highest exponent. Ready for the (bloody) next step? :)

Answer 48

oh I see hahaha....

Answer 49

Okay... now to the annoying rational root test... did Kurt already take this up with you?

Answer 50

He did but I was too selepy to listen to him..... Actually he too was sleepy that night...

Answer 51

Sounds like him all right. Anyway, you need the factors of the leading coefficient and the constant.
What are the leading coefficient and constant in the equation
\[\large 4z^5-20z^4+35z^3-31z^2-9z + 9=0\]
?

Answer 52

You haven't the slightest idea what I'm talking about... have you? :P

Answer 53

I do :)

Answer 54

wait still thinking

Answer 55

Leading coefficient is the coefficient of the z with the largest exponent. 4, right? :)

Answer 56

Not to be rude or anything, but you're gonna have to hurry it up, I got school lol

Answer 57

Who needs to go to school? :P

Answer 58

yeah you of course hahah

Answer 59

MAybe Kurt can handle me now...

Answer 60

Well pardon me if I'm no super-genius, Kurt Rainer :P

Answer 61

Run along now :)

Answer 62

riiiiiight
see ya kuya Kurt...
Josh... a little faster next time? haha

Answer 63

olryt

Answer 64

Now where was I... Oh yes, leading coefficient. It's 4, right?