# How do you find the discriminant and how many and what type of solutions does 2x^2+5x+3=0 have?

May 9, 2015

Your equation is in the form: $a {x}^{2} + b x + c = 0$
Where:
$a = 2$
$b = 5$
$c = 3$
The discriminant is:
$\Delta = {b}^{2} - 4 a c = 25 - 4 \left(2 \cdot 3\right) = 25 - 24 = 1 > 0$
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.