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)   (Show Source): You can put this solution on YOUR website!
when the discriminant is less than zero you get two complex solutions
:
would be one such example
:

:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

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 - .

The solution is , or
Here's your graph:
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