Quick! Polynomial question!

[GameGURU]

Ok, I am sorta lost here.

I am currently supposed to find the roots of a Polynomial function. I know what a polynomial is and what a function is, that's not the problem. The problem is that I have no idea how to get the other 2 roots of, say, a 3rd degree equation if I am given one root.

Say I have the function:

f(x)=x^3-4x^2+6x-4

One root is: 2

We know that -2 is also a root, becuase that's just the way it is. So, onto the last root.

How do I plug 2 into the equation to get the last root? My book only gives me a shoddy example of some other type of problem (involving an imaginary), so that's not much help here.

Common then, I know some of ya are math wizards. Please help me out, I would be most gracious

 

[Chankama]

Known:
f(x)=x^3-4x^2+6x-4
x=2 is a root, i.e. f(2) = 0

Procedure:
Divide f(x) by (x-2) - since f(x) = (x-2)(......) = 0 = f(2), when x=2
We need to find what's in the (......)

I use long division (in this case just do it in my head ), but you can use synthetic division or whatever.

f(x) = (x-2)(x^2-2x+2)

Find the roots of (x^2-2x+2) - easy to do.

So I guess roots = 2, 1 +- i, where +- is plus/minus

 

[Chankama]

Just noticed you saying this:

We know that -2 is also a root, becuase that's just the way it is. So, onto the last root.

That's not true.

 

[GameGURU]

Hmm my book and teacher said that the inverse of the given root is also a root.

Or does that just apply if our root is say, x-4 ?

 

[Chankama]

Hmm my book and teacher said that the inverse of the given root is also a root.

Then he/she would be wrong and the book is wrong too. Maybe that's where the teacher got it from. Are you interpreting them correctly?

I can create any artibrary polynomial I want to.

Pick any 3 terms: (x-3), (x-1000), (x+20) and multiply them together.

f(x) = (x-3)(x-1000)(x+20)

What are the roots?

None of them are inverses of each other!

 

[Flanker]

And yet it never ceases to amaze me;

I R TEH STUPID....CHANKAMA R TEH SMART

Getting old? Ok, I'll stop.

 

[Chankama]

LOL.. Nubius is probably thinking "That d*** Flanker!!".

 

[Nubius]

nah lol, Flanker has yet to completely over use it and each time he uses it has been perfectly placed, so it's definitely ok for now

I'm glad my comment can make some laughs TIME and TIME again.

You need to have Havoc make you a userbar that says "Math Professor" or "Math Wizard" if you want to go a little fruit, or perhaps even further "MATHEMAGICIAN!"

I just did this stuff last semester, but I need to see the book.........scan the page in yo

 

[Emily]

Hmm my book and teacher said that the inverse of the given root is also a root.

Or does that just apply if our root is say, x-4 ?

That's true for imaginary roots... if i+2 is a root then i-2 is a root also.

Chankama how do you remember high school math so well? It kind of freaks me out.

 

[Chankama]

That's true for imaginary roots... if i+2 is a root then i-2 is a root also.

Not in the general case. ..

It's only true if the coefficients of the expanded polynomial are "real numbers".

b/c I can just make a new polynomial: f(x) = (x+2)(x+2i)(x-3i)(2x+i), where none of the terms are conjugates of each other.

Chankama how do you remember high school math so well? It kind of freaks me out.

LOL.. Yeah it's been a while. .. But, I've done so many math contests way back when, it's difficult to forget this stuff even if I wanted to. hehehehehe

You need to have Havoc make you a userbar that says "Math Professor" or "Math Wizard" if you want to go a little fruit, or perhaps even further "MATHEMAGICIAN!"

LOL.. If I take a walk in downtown, wearing a t-shirt that says "TF MATHEMAGICIAN!" in big fruity letters, wonder how many eggs I'll get thrown at my face..
:grind: