SOLUTION: Solve the equation x^2-4x+2=0 , if possible. Write irrational numbers in simplest radical form. Describe the strategy you used to get your solution and tell why you chose that stra

Algebra ->  Finance -> SOLUTION: Solve the equation x^2-4x+2=0 , if possible. Write irrational numbers in simplest radical form. Describe the strategy you used to get your solution and tell why you chose that stra      Log On


   

Question 1140443: Solve the equation x^2-4x+2=0 , if possible. Write irrational numbers in simplest radical form. Describe the strategy you used to get your solution and tell why you chose that strategy.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation x^2-4x+2=0 , if possible. Write irrational numbers in simplest radical form.
------
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B2+=+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=%28-4%29%5E2-4%2A1%2A2=8.

Discriminant d=8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+8+%29%29%2F2%5C1+=+3.41421356237309
x%5B2%5D+=+%28-%28-4%29-sqrt%28+8+%29%29%2F2%5C1+=+0.585786437626905

Quadratic expression 1x%5E2%2B-4x%2B2 can be factored:
1x%5E2%2B-4x%2B2+=+%28x-3.41421356237309%29%2A%28x-0.585786437626905%29
Again, the answer is: 3.41421356237309, 0.585786437626905. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B2+%29

==================
Describe the strategy you used to get your solution and tell why you chose that strategy.
----
Get someone to do it for me.