Last day of 2015 problem
Sriram says to Hari, " I am thinking of polynomial whose roots are all positive integers. The polynomial has the form \(P(x)=2x^3-2ax^2 +(a^2-81)x-c\) for some positive integers \(a\) and \(c\). Can you tell me the values of \(a\) and \(c\) ? "
After some calculations, Hari says, " There is more than one such polynomial."
Sriram says, " You're right. Here is the value of \(a\)." He writes a positive integer and asks, " Can you find the value of \(c\) ? "
Hari says, " There are still two possible values of c ."
Find the sum of two possible values of c.