SOLUTION: Could someone help me find the complex solution of the following: a. 2x^2 + 3 = 3x b. 1/2x^2 - 5x + 13 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Could someone help me find the complex solution of the following: a. 2x^2 + 3 = 3x b. 1/2x^2 - 5x + 13 = 0      Log On


   

Question 25954: Could someone help me find the complex solution of the following:
a. 2x^2 + 3 = 3x
b. 1/2x^2 - 5x + 13 = 0
Answer by elephantsize(7) About Me  (Show Source):
You can put this solution on YOUR website!
b)
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 0.5x%5E2%2B-5x%2B13+=+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=%28-5%29%5E2-4%2A0.5%2A13=-1.

The discriminant -1 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 -1 is + or - sqrt%28+1%29+=+1.

The solution is x%5B12%5D+=+%28--5%2B-i%2Asqrt%28+-1+%29%29%2F2%5C0.5+=++%28--5%2B-i%2A1%29%2F2%5C0.5+, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.5%2Ax%5E2%2B-5%2Ax%2B13+%29