1. The problem statement, all variables and given/known data In problem 1.18.b of Calculus, he says: . (Bold mine). I assume that is supposed to say in fact x2+bx+c>0 ? However, I am having trouble proving that for all choices of b and c. If I complete the square on x2+bx+c>0 I get x2+bx+c = (x+b/2)2 + k > 0 => k > 0. So I have that k = c - b2/4 > 0. But I don't know that this is true for all b,c.