SOLUTION: Find the imaginary solutions of the equation. {{{5x^2+3x+6=0}}}

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Question 48446: Find the imaginary solutions of the equation.
5x%5E2%2B3x%2B6=0
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
5x^2 + 3x + 6 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B3x%2B6+=+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%2A5%2A6=-111.

The discriminant -111 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 -111 is + or - sqrt%28+111%29+=+10.5356537528527.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B3%2Ax%2B6+%29