SOLUTION: For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary t      Log On


   

Question 234854: For this problem I need to use the discriminate to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. It is not necessary to find the roots; just determine the number and types of solutions
2x^2-6x+5=0
Answer by philline_palana(20) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-6x%2B5+=+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=%28-6%29%5E2-4%2A2%2A5=-4.

The discriminant -4 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 -4 is + or - sqrt%28+4%29+=+2.

The solution is x%5B12%5D+=+%28--6%2B-+i%2Asqrt%28+-4+%29%29%2F2%5C2+=++%28--6%2B-+i%2A2%29%2F2%5C2+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-6%2Ax%2B5+%29