Math Is Fun Forum

the_conjecturer

Guest

can't prove this conjecture

hello,

can anyone find any way that i might be able to prove this conjecture (i made this when thinking about sequences);

The polynomial equation

has no real solutions greater than 2.

is there any way to prove this?

the_conjecturer

Guest

Re: can't prove this conjecture

in case its unclear, what i mean is for example, if you have the equation

x^30 - x^29 - x^28 ... - x - 1 = 0

the real solutions for x dont exceed 2. and i conjecture it wont for a polynomial of order n, no matter how large n is, for example, 3000, or 10000000000, or whatever.

but how do i prove this?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: can't prove this conjecture

Hi the_conjecturer;

The simplest way is to make use of the theory of equations. Bounds can be put on roots of a polynomial. Take a look here and apply that to the general polynomial you have.

http://www.mathsisfun.com/algebra/polyn … zeros.html

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.