I'm trying to find upper and lower bounds of the smallest positive root of a polynomial, stated in terms of its coefficients. As I appreciate it might be a very general problem, My specific interest is in polynomials of the sort
$$ -ax^q + bx^p -c = 0 \, \quad a,b,c>0\, , \quad q>p \, .$$
I know that, under some restrictions, it has real positive roots, and so I'd be interested in either-
- Upper and lower bounds on the smallest positive root.
- Upper and lower bounds of all real roots.
- Upper and lower bounds for all positive roots.
- Bounds on the roots of a general polynomial.
- Bounds for the specific case $q=p+1$.
Thanks
Amir