# How to use the discriminant to find out how many real number roots an equation has for a^2 + 12a + 36 = 0?

May 20, 2018

The discriminant is: ${b}^{2} - 4 a c$

$a = 1$
$b = 12$
$c = 36$

Substitute these values into the discriminant and you should get two answers (real roots):

${12}^{2} - 4 \left(1\right) \left(36\right) = 0$

If the discriminant is 0 there is 1 real root, if it is > 0 there are 2 and otherwise 0 real roots.

May 20, 2018

one at $x = - 6$

#### Explanation:

$a {x}^{2} + b x + c$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

discriminant is the part under the square root: ${b}^{2} - 4 a c$

if discriminant < 0 there are 2 imaginary roots
if discriminant > 0 there are 2 real roots
if discriminant = 0 there is 1 real root
if discriminant is a perfect square roots are rational

for yours:

a = 1
b = 12
c = 36

${12}^{2} - 4 \cdot 1 \cdot 36 = 0$

since the discriminant is 0 the function has 1 real root at $- \frac{b}{2} a$

$x = - 6$

graph{x^2+12x+36 [-13.79, 6.21, -0.92, 9.08]}