Christmas Contest - Team Round - Problem 4

Excelex and Geeks are on a 100-day math training arcs in the hopes of qualifying USAJMO. Let E(x) and G(x) be the number of hours grinded in day x for Excelex and Geeks, respectively.

Suppose that E(x) = 4x^2-16x+17 and G(x) = 3x^2+bx+c, the domain of both functions is the set of all integers from 1 to 100, inclusive. Let day a be the day where Excelex grinded the minimum amount of hours over all values of x in his domain.

Coincidentally, day a is also the day where Geeks grinded his minimum amount of hours. Furthermore, Excelex and Geeks both grinded d hours this day. With this information, compute a+b+c+d.