Question

What is the symmetric function for \(α^5+β^5\)?

Answer 1

Where \(\alpha\) and \(\beta\) are roots of a quadratic polynomial.

Answer 2

I believe it is the expansion of that and then substituting the values for \(\alpha + \beta \) and \(\alpha\beta\)

Answer 3

I don't know, I have no idea about this.

Answer 4

I don't even know what question means. If someone could explain me the question.

Answer 5

i cant make any sense of what google has to offer in this

Answer 6

All quadratic functions are symmetric, right?
\[(x-a)(x-b)=0\]
\(a\) and \(b\) are the roots and that's all I can make out of it.

Earlier FoolForMath posted a definition "A function of α and β is said to be symmetric if it remains unchanged when α and β are interchanged".

Answer 7

but it is not asking for symmetric function of the quadratic equation

Answer 8

Symmetric function of roots: A functions of α and β is said to be symmetric if it's remain unchanged when α and β are interchanged.

\[ α^5+β^5 = (α^3+β^3)(α^2+β^2)-α^2β^2(α+β) \]

Answer 9

Unrelated Fun: http://www.damnlol.com/i/7355afe7994b2baf4125c449794140c6.jpg

Answer 10

But what does this Graphically imply?

And what is \(\alpha^5+\beta^5\)? I can a plot a function and show \(\alpha\) and \(\beta\) but I don't a thing what \(\alpha^5+\beta^5\) or \(|\alpha + \beta|\) is.

Answer 11

"...I don't know* a thing..."

Answer 12

I am not aware of any graphical significance but I have used it some problems where a quadratic equation is given and we need find these ...

Answer 13

Oh :-( then I guess I would remain confused about this concept

Answer 14

btw FoolForMath what is the function?
\(↓ ↓ \) This is just a algebraic manipulation, right? This can't be a function?!
\[α^5+β^5 = (α^3+β^3)(α^2+β^2)-α^2β^2(α+β)\]

Answer 15

What do you after the manipulation, do you replace the \(\alpha\) and \(\beta\) using sums and products property of a quadratic expression?

Answer 16

why does amistre have to mention google in his answers lol, is it some fun fashion kinda thing with respect to answering questions?

Answer 17

But even if you replace the α and β using sums and products property of a quadratic expression, you won't get a function. You will only get a constant value. So what is the function?

Answer 18

this is quite messy lol

Answer 19

I don't really understand the question, could you explain?

Answer 20

Yeah, at least for me it is. @saso


Me neither Mr.Math, FoolForMath asked this question [at] http://openstudy.com/users/sasogeek#/updates/4f3f4c0ae4b0534c53cbbc1d

Answer 21

The question doesn't make sense to me. We can write a function \(f(\alpha,\beta)=\alpha^5+\beta^5.\) This function is symmetric since \(f(\alpha,\beta)=f(\beta,\alpha) \) for all \(\alpha\) and \(\beta\) in the domain of \(f\).
But I don't see this answers the question that I don't understand :-D

Answer 22

But αand β are constants, why would they ever make a function?

Answer 23

Oh.

Answer 24

Where α and β are roots of a quadratic polynomial.

Answer 25

I can't find my question paper, else I would have posted one example problem.

Answer 26

Maybe I am overthinking this :-/

Answer 27

yes you are.

Answer 28

Yes, I think there's something missing in the question.