SOLUTION: I have the answer to this problem but I am not sure how they got it... g(x)= 4x^2 - 3x + 1 answer; 3/8 +- square root (7)/8i Can someone explain how they did this? Thank you

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I have the answer to this problem but I am not sure how they got it... g(x)= 4x^2 - 3x + 1 answer; 3/8 +- square root (7)/8i Can someone explain how they did this? Thank you      Log On


   



Question 559483: I have the answer to this problem but I am not sure how they got it...
g(x)= 4x^2 - 3x + 1
answer;
3/8 +- square root (7)/8i
Can someone explain how they did this?
Thank you

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
g(x)= 4x^2 - 3x + 1
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-3x%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=%28-3%29%5E2-4%2A4%2A1=-7.

The discriminant -7 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 -7 is + or - sqrt%28+7%29+=+2.64575131106459.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-3%2Ax%2B1+%29