SOLUTION: I had a test question and it was 5w(squared)-2w+4=0 and it told me to find the Discriminant, the nature of the roots, the exact solution and the approx solution. i found the discr

Algebra ->  Test -> SOLUTION: I had a test question and it was 5w(squared)-2w+4=0 and it told me to find the Discriminant, the nature of the roots, the exact solution and the approx solution. i found the discr      Log On


   

Question 23720: I had a test question and it was 5w(squared)-2w+4=0 and it told me to find the Discriminant, the nature of the roots, the exact solution and the approx solution. i found the discriminat to be the squareroot of -76...I thought the nature of the roots was down because it was negitive. please help im stumped! i dont have the best teacher an he cant really explain things well and idnt even know what i was supposed to write for the approx. solution. HELP!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
You have a quadratic equation with a=5, b=-2, c=4
When the discriminant is negative that means the
two solutions are complex numbers. See the following:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case 5w%5E2%2B-2w%2B4+=+0) has the following solutons:

w%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=%28-2%29%5E2-4%2A5%2A4=-76.

The discriminant -76 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 -76 is + or - sqrt%28+76%29+=+8.71779788708135.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-2%2Ax%2B4+%29


Cheers,
Stan H.