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

2 Answers
May 20, 2018

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.

May 20, 2018

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]}