SOLUTION: What type of solutions do you get from a quadratic equation where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation and find the solutions o

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Question 194126: What type of solutions do you get from a quadratic equation where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation and find the solutions of the equation. Thank You
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
when the discriminant is less than zero you get two complex solutions
:
x%5E2%2B3x%2B7=0 would be one such example
:
3%5E2-4%281%29%287%29=-19
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B7+=+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%2A7=-19.

The discriminant -19 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 -19 is + or - sqrt%28+19%29+=+4.35889894354067.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B7+%29