I'm trying to find upper and lower bounds of the positive value 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-

1. Upper and lower bounds of all real roots.
2. Upper and lower bounds for positive roots.
3. Bounds on the roots of a general polynomial.
4. Bounds for the specific case $q=p+1$.

Thanks

Amir

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-

1. Upper and lower bounds on the smallest positive root.
2. Upper and lower bounds of all real roots.
3. Upper and lower bounds for all positive roots.
4. Bounds on the roots of a general polynomial.
5. Bounds for the specific case $q=p+1$.

Thanks

Amir