Does anybody know how to solve this?
Let $f(x) = x^2 + 6x + c$ for all real numbers $x$, where $c$ is some real number. For what values of $c$ does $f(x) = 0$ have exactly $2$ distinct real roots?
This will have two distinct roots when the discriminant > 0
6^2 - 4 (1)(c) > 0
36 - 4c > 0
36 > 4c
36/4 > c
9 > c
It will have two distinct roots when c < 9