The Strange Function

Chef has found a strange function F on his way home. It has the form of F(x) = ax2 + bx + c√x. Here √x denotes the positive square root of x. On returning home he begins putting various values as x and sees the results. Chef likes integers, and sometimes the result turns out to be an integer, but sometimes it does not. So Chef starts thinking of the reverse operation. If Chef desires a particular