SOLUTION: how do you find the discriminant and tell the number of solutions of the equation??? 5x^2 - 2x +2 = 0 its algebra 2

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Question 187481: how do you find the discriminant and tell the number of solutions of the equation???

5x^2 - 2x +2 = 0

its algebra 2
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
how do you find the discriminant and tell the number of solutions of the equation???
5x^2 - 2x +2 = 0
That's well covered in the onsite solver:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-2x%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=%28-2%29%5E2-4%2A5%2A2=-36.

The discriminant -36 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 -36 is + or - sqrt%28+36%29+=+6.

The solution is x%5B12%5D+=+%28--2%2B-i%2Asqrt%28+-36+%29%29%2F2%5C5+=++%28--2%2B-i%2A6%29%2F2%5C5+, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-2%2Ax%2B2+%29

Ignore what it says about factoring.
You can reduce it further:
(1+3i)/5
(1-3i)/5