Francois Vieta
 

Here's a different kind of math problem.

I post you a link to a page on [url=http://mathworld.wolfram.com/VietasFormulas.html] Mathworld[/url] and you have to find the mistake.

good luck.

[spoiler]"products of distinct polynomial roots r_j"[/spoiler]
[spoiler]seems improperly worded to me since x^2+4x+4 has only the root 2, but a root product of 4[/spoiler]

Don't we have LaTeX on here now?

[quote=tom11784]Don't we have LaTeX on here now?[/quote]
Yes, we do.

Since your polynomial is of degree 2 it must have 2 roots. When the discriminant = 0, as in this case, both roots are the same; [tex]2\, \times \,2 \,= \,4[/tex].

that's exactly my point - it's for distinct j of r_j, not distinct r_j

[QUOTE=tom11784]that's exactly my point - it's for distinct j of r_j, not distinct r_j[/QUOTE]
What it actually says is:
[quote=Mathworld]Let s_i be the sum of the products of distinct polynomial roots r_j of the polynomial equation..."[/quote]
The way I read this, and I am more than happy for someone to correct me if I am wrong, is that r_j is defined as the product of distinct roots. Since you can't have a product of one number, that must mean roots plural. Since roots always come in pairs (real ones do, anyway) I read this as meaning that r_j is the product of one pair of roots. I guess the next pair would be r_k, then s_i = r_j + r_k etc. until you have i terms in the sum.

If you feel strongly that this is ambiguous, or poorly worded or whatever please feel free to email the folks at Mathworld about it. Needless to say, it is not the mistake I was talking about.

Are you talking about the typos or the basic facts?

"This can be seen for a second-polynomial degree polynomial by multiplying out" is obviously a typo. How the heck can one polynomial be the degree of another? They would always simplify to being based on the highest terms.

I'll read it some more to find other less-insanifying mistakes.

[QUOTE=nibble4bits]I'll read it some more to find other less-insanifying mistakes.[/QUOTE]
Insanifying !??!?

If nothing else we are going to extend the vocabulary somewhat. But strangely enough I knew exactly what you meant.

No, this is not it either.

Insanify: To force to insanity. To make someone think "What the?!"
LOL
It's what I say when something just plain seems to make the opposite of sense. Used by local tecnicians to describe something designed by someone with schitzoid-inspiring skills.

Francois Vieta
 

[QUOTE=Numbers]Yes, we do.

Since your polynomial is of degree 2 it must have 2 roots. When the discriminant = 0, as in this case, both roots are the same; [tex]2\, \times \,2 \,= \,4[/tex].[/QUOTE]
:rolleyes:
The roots are -2 ; -2 and not 2 ;2
For the quadratic ax^2 + bx + c the roots are given as
[- b +- sq.rt (b^2.- 4ac)]/2a
When the discriminant is = 0 the root becomes - b/2a
If you substitute 2 in x^2 + 4x +4 you get 16 and NOT 0
-2 on the other hand gives 0
Mally :coffee:

As it doesn't look like anyone is going to get this any time soon, here is the answer.

[spoiler]Mathworld says that Vieta proved this formula (for positive roots only)[/spoiler]
[spoiler]in 1646. Pretty good going for a guy who had been dead for 43 years.[/spoiler]

[QUOTE=Numbers]As it doesn't look like anyone is going to get this any time soon, here is the answer.

[spoiler]Mathworld says that Vieta proved this formula (for positive roots only)[/spoiler]
[spoiler]in 1646. Pretty good going for a guy who had been dead for 43 years.[/spoiler][/QUOTE]
:smile:

Viete , Francois (Franciscus Vieta ) (1540 -1603 ) French mathematician.
cian
Viete wrote a number of topics on Maths which were published posthumously.
For instance his 'article' "The mathematical recognition and Emendation of Equations" was published in 1615 i.e. 12years after his death.
Ref: "A short account of the History of Mathematics" by W.W. Rouse Ball.
"Dictionary of Mathematics" Penguin.
Mally :coffee:

[QUOTE=Numbers]As it doesn't look like anyone is going to get this any time soon, here is the answer.

[spoiler]Mathworld says that Vieta proved this formula (for positive roots only)[/spoiler]
[spoiler]in 1646. Pretty good going for a guy who had been dead for 43 years.[/spoiler][/QUOTE]
To paraphrase Tom Lehrer: it makes me realise how little I've achieved when I think that by the time Alan Turing was my age he'd been dead for 5 years.


Paul

Francois Vieta
 

[QUOTE=xilman]To paraphrase Tom Lehrer: it makes me realise how little I've achieved when I think that by the time Alan Turing was my age he'd been dead for 5 years.
Paul[/QUOTE]
:smile:
In my book it is the effort that counts not the results
Mally :coffee:

[QUOTE=nibble4bits]Insanify: To force to insanity. To make someone think "What the?!"
[/QUOTE]

The opposite of sensiblise, then?

[QUOTE=fatphil]The opposite of sensiblise, then?[/QUOTE]
I spell it with a 'ize' but yes. heh