Let f(x) = x^3 + bx + c, where b and c are integers. If f(\sqrt{5}) = 0, determine b + c.
f(sqrt 5) = 0
So
(sqrt 5)^3 + b(sqrt 5) + c = 0
5sqrt 5 + bsqrt (5) + c = 0
One possibility
b = -5 c = 0
b + c = -5
+1725 
