SOLUTION: I need to solve this one and I need help: I have to apply the quadratic formula to find the roots of the given function, and then graph the function. g(x) = x^2 + x + 12

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I need to solve this one and I need help: I have to apply the quadratic formula to find the roots of the given function, and then graph the function. g(x) = x^2 + x + 12      Log On


   

Question 36348: I need to solve this one and I need help: I have to apply the quadratic formula to find the roots of the given function, and then graph the function.

g(x) = x^2 + x + 12
Found 2 solutions by cininnatus, Alwayscheerful:
Answer by cininnatus(12) About Me  (Show Source):
You can put this solution on YOUR website!
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1
b=1
c=12
The graph looks like a parabola

Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2Bx%2B12=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B12+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%281%29%5E2-4%2A1%2A12=-47.

The discriminant -47 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -47 is + or - sqrt%28+47%29+=+6.85565460040104.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B12+%29

Hope this helps!