SOLUTION: What is 3g^2+g+1 factored.

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Question 36174: What is 3g^2+g+1 factored.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
What is 3g^2+g+1 factored.
a=3, b=1, c=1
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B1x%2B1+=+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%2A3%2A1=-11.

The discriminant -11 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 -11 is + or - sqrt%28+11%29+=+3.3166247903554.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B1%2Ax%2B1+%29


Factors are
(x-[-1+sqrt(-11)]/2)(x-[-1-sqrt(-11)]/2)
Hope this helps.
cheers,
Stan H.