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 th

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Question 171185: 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. I am confused I always thought it was Ax^2 +Bx +C=0, am I missing something in this question? Please help
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
The D they are referring to is the Determinant of the quad. It is found by using the coefficents of the standard form. When D<0 you get 2 complex roots for a solution.
:
D = b2 - 4ac
:
example of an equation that gives a negative D....x%5E2-4x%2B13=0
D = b2 - 4ac
= (-4)2 - 4(1)(13) = -36
:
solutionsystem%282%2B3i%2C2-3i%29
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%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=%28-4%29%5E2-4%2A1%2A13=-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--4%2B-+i%2Asqrt%28+-36+%29%29%2F2%5C1+=++%28--4%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-4%2Ax%2B13+%29