Chapter 4 Quadratic Functions and Factoring - 4.8 Use the Quadratic Formula and the Discriminant - 4.8 Exercises - Skill Practice - Page 297: 61

$2$ solutions if $1\gt c$, one solution if $1=c$, and no solution if $1\lt c$

The discriminant is $D=b^2-4ac$. If $D\gt0$ we have $2$, if $D=0$ we have one, if $D\lt0$ we have no solution. Hence here $D=1-c$. $1-c\gt0\\1\gt c.$ $1-c=0\\1= c.$ $1-c\lt0\\1\lt c.$ Thus we have $2$ solutions if $1\gt c$, one solution if $1=c$, and no solution if $1\lt c$.