Question

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

Answer 1

The discriminant is: `b^2-4ac`

`a=1`
`b=12`
`c=36`

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

`12^2-4(1)(36) = 0`

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

Answer 2

one at `x= -6`

Explanation:

`ax^2+bx+c`

Quadratic formula:

`x = (-b+-sqrt(b^2 - 4ac))/(2a)`

discriminant is the part under the square root: `b^2-4ac`

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*1*36=0`

since the discriminant is 0 the function has 1 real root at `-b/2a`

`x= -6`

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