How to use the discriminant to find out how many real number roots an equation has for a2+12a+36=0?

2 Answers

The discriminant is: b24ac

a=1
b=12
c=36

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

1224(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:

ax2+bx+c

Quadratic formula:

x=b±b24ac2a

discriminant is the part under the square root: b24ac

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

1224136=0

since the discriminant is 0 the function has 1 real root at b2a

x=6

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