# What is the discriminant of x^2 + 8x + 16 = 0 and what does that mean?

Jul 23, 2015

The expression is of the form $A {x}^{2} + B x + C = 0$
where $A = 1 , B = 6 , C = 16$

#### Explanation:

The discriminant is defined as $D = {B}^{2} - 4 A C$
If $D > 0$ there are two solutions to the equation
If $D = 0$ there is one solution
If $D < 0$ there is no solution (in real numbers)

In your case $D = {8}^{2} - 4 \cdot 1 \cdot 16 = 0 \to$one solution.

The equation can be written as ${\left(x + 4\right)}^{2} \to x = - 4$