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

2 Answers

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

Answer:

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]}