A mean mean polynomial

Note that the roots of a degree 5 polynomial, $a,b,c,d$ and $e$ will all be the constant term of the polynomial in the form of $-abcde$ therefore $P(0)=-abcde=-32768$ . Therefore taking the 5th root of $abcde$ gives us $\sqrt[5]{32768}=2^{15/5}=8$ . This is the geometric mean of our roots which is our lower bound of $m$ because of the AM-GM inequality. This means that we have to find the mean of the numbers 8-99 inclusive.

First we sum from 1 to 99 and subtract the sum 1 to 7. To get 4929 by using triangle numbers. Then by dividng by 99-8=91 we have $\frac{4929}{91}$ then convert to a mixed fraction to get $54\frac{15}{91}$ and flooring this removes the proper fractional part. Finally giving us $\boxed{54}$ .