Chapter 4 Quadratic Functions and Factoring - 4.8 Use the Quadratic Formula and the Discriminant - 4.8 Exercises - Skill Practice - Page 297: 58

$2$ solutions if $-64\lt c$, one solution if $-64=c$, and no solution if $-64\gt c$.

The discriminant is $D=b^2-4ac$. If $D\gt0$ we have $2$, if $D=0$ we have one, and if $D\lt0$ we have no solution. Hence here $D=256+4c$. $256+4c\gt0\\256\gt-4c\\-64\lt c.$ $256+4c=0\\256=-4c\\-64= c.$ $256+4c\lt0\\256\lt-4c\\-64\gt c.$ Thus we have $2$ solutions if $-64\lt c$, one solution if $-64=c$, and no solution if $-64\gt c$.