lower bound for absolute values of zeroes of polynomial with non-zero constant term

I know there are upper bounds for the absolute value of polynomial zeroes. I have polynomials with non-zero constant terms. How can I find lower bounds for the absolute values of their zeroes? I don't think I need very good bounds, simple ones should do.

Re: lower bound for absolute values of zeroes of polynomial with non-zero constant te

If with and is a root of then, easily proved where

Re: lower bound for absolute values of zeroes of polynomial with non-zero constant te

Thank you. I didn't know this bound.

I was asking about something slightly different though. Let and be defined as above, but with Now I'd like to find such that

Re: lower bound for absolute values of zeroes of polynomial with non-zero constant te

Quote:

Originally Posted by

**ymar** I was asking about something slightly different though. Let

and

be defined as above, but with

Now

I'd like to find

such that

Use the substitution and you'll have a bound of the form where now corresponds to .

Re: lower bound for absolute values of zeroes of polynomial with non-zero constant te

I provide a proof of the result in answer #2. Suppose , then

That is, if then , so is not a root of .