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

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Question 170718This question is from textbook Intermediate algebra
: What type of solution do you get for quadratic equations where D<0?
Give reasons for your answer.
Also provide an example of such a quadratic equation and find the solution of the equation.
This question is from textbook Intermediate algebra

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
D=b2- 4ac if the discriminant is less than zero you will have complex roots.
:
where ax%5E2%2Bbx%2Bc=0

x%5E2-10x%2B34=0example of negative determinant
:
D=(-10)^2-4(1)(34)=-36
solution 5+3i and 5-3i
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-10x%2B34+=+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=%28-10%29%5E2-4%2A1%2A34=-36.

The discriminant -36 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 -36 is + or - sqrt%28+36%29+=+6.

The solution is x%5B12%5D+=+%28--10%2B-+i%2Asqrt%28+-36+%29%29%2F2%5C1+=++%28--10%2B-+i%2A6%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B34+%29