SOLUTION: {{{ g(x)=x^2+X+12 }}} Use the quadratic formula to find the roots I get a=1 b=1 and c=12 If I'm doing this right I'm getting roots of {{{ -1+i * sqrt47/2 }}} and {{{-1-i *

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: {{{ g(x)=x^2+X+12 }}} Use the quadratic formula to find the roots I get a=1 b=1 and c=12 If I'm doing this right I'm getting roots of {{{ -1+i * sqrt47/2 }}} and {{{-1-i *      Log On


   

Question 461037: +g%28x%29=x%5E2%2BX%2B12+ Use the quadratic formula to find the roots
I get a=1 b=1 and c=12
If I'm doing this right I'm getting roots of +-1%2Bi+%2A+sqrt47%2F2+ and -1-i+%2A+sqrt+47%2F2+
Am I right? If so, I do I plug that into the original formula to check the answers (as required in my class)?

Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
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