# Thread: rational roots b/c

1. ## rational roots b/c

Hi;
When determining rational roots of a polynomial ie b/c or b/q which one is correct
and what do the letters mean?

Thanks,

2. ## Re: rational roots b/c

Originally Posted by anthonye
Hi;
When determining rational roots of a polynomial ie b/c or b/q which one is correct
and what do the letters mean?
most texts use $\displaystyle \frac{p}{q}$, though it doesn't really matter what letters are used ...

Mathwords: Rational Root Theorem

3. ## Re: rational roots b/c

So the letters don't stand for anything then?

4. ## Re: rational roots b/c

For a polynomial in the form $\displaystyle a_n x^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0 = 0$, where $\displaystyle a_i \in \mathbb{Z}$, all possible rational roots are in the form $\displaystyle \frac{p}{q}$, where $\displaystyle p$ is a factor of the constant coefficient $\displaystyle a_0$ and $\displaystyle q$ is a factor of the leading coefficient $\displaystyle a_n$. Very easy to prove.

5. ## Re: rational roots b/c

The letters are arbitrary. They don't really stand for anything.

6. ## Re: rational roots b/c

Thanks thats what I was after.