A polynomial f with integer coefficients is written on the blackboard. The teacher is a mathematician who has 3 kids: Andrew, Beth and Charles. Andrew, who is 7, is the youngest, and Charles is the oldest. When evaluating the polynomial on his kids' ages he obtains:
f(7)=77
f(b)=85, where b is Beth's age,
f(c)=0, where c is Charles' age.
How old is each child? algebrapolynomialalgebra unsolved