Let b and c be integers in the set \({-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}\) (Note that b and c can be equal.) For how many choices of b and c is it true that the roots of \(x^2 + bx + c\) are consecutive integers?
There are 6 + 7 + 8 = 21 choices for b and c.
