2. (7 points) It is known that $a+b+c<0$ and that the equation $a x^{2}+b x+c=0$ has no real roots. Determine the sign of the coefficient $c$.


Solution. Let $y=a x^{2}+b x+c$, then $y(1)=a+b+c, y(1)<0$.

Since the equation $a x^{2}+b x+c=0$ has no real roots, the branches of the parabola are directed downwards and then $c<0$.

Answer. $c<0$.