The square trinomial $y=ax^2 + bx + c$ has no roots and $a + b + c > 0$. Find the sign of the coefficient $c$. I'm having difficulties with this problem.
What I've tried: I realized that a quadratic equation doesn't have roots if the discriminant $b^2 - 4ac < 0$, so I've tried to combine that with the condition $a + b + c > 0 <=> a > -b -c $, but that didn't help me that much.
I would appreciate if someone could help me to understand this. I'll ask a lot of questions on this network while I'm learning, so please don't judge me for that :) .