SOLUTION: Someone, please show me how to find the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. The only thing

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Someone, please show me how to find the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. The only thing       Log On


   

Question 144440: Someone, please show me how to find the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. The only thing i need to do is find the number and types of solutions.
(3)1/2y2 - 4y - 7(3)1/2 = 0. i would appreciate any help i can get. Thank you in aadvance.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
example:
x%5E2+%2B+3x+-+2+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-2+=+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=%283%29%5E2-4%2A1%2A-2=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+17+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+17+%29%29%2F2%5C1+=+0.56155281280883
x%5B2%5D+=+%28-%283%29-sqrt%28+17+%29%29%2F2%5C1+=+-3.56155281280883

Quadratic expression 1x%5E2%2B3x%2B-2 can be factored:
1x%5E2%2B3x%2B-2+=+%28x-0.56155281280883%29%2A%28x--3.56155281280883%29
Again, the answer is: 0.56155281280883, -3.56155281280883. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-2+%29