# How do you find the discriminant and how many solutions does r^2=3r+0 have?

May 9, 2015

Your equation, written as ${r}^{2} - 3 r = 0$ is in the form: $a {x}^{2} + b x + c = 0$
Where:
$a = 1$
$b = - 3$
$c = 0$
The discriminant is:
$\Delta = {b}^{2} - 4 a c = 9 - 4 \left(1 \cdot 0\right) = 9 > 0$
Now, if:
1] $\Delta > 0$ you have 2 distinct Real solutions;
2] $\Delta = 0$ you have two Real coincident solutions;
3] $\Delta < 0$ you have no Real solutions.