# How do you find the discriminant of x^2+4x+3=0 and use it to determine if the equation has one, two real or two imaginary roots?

Mar 7, 2017

$D = {B}^{2} - 4 A C$
Where $A , B , C$ are numbers from left to right in an ordered equation.

#### Explanation:

$D = {4}^{2} - 4 \cdot 1 \cdot 3 = 16 - 12 = 4$

$D > 0 \to$ two real solutions ($x = - 1 \mathmr{and} x = - 3$)
$D = 0 \to$ one real solution
$D < 0 \to$ two imaginary solutions
graph{x^2+4x+3 [-10.53, 5.27, -1.447, 6.45]}