SOLUTION: I need someone help I'm totally stuck. please please help. Thank you. What type of solution do you get for quadratic equations where D < 0? Give reasons for your answer. Also

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Question 172401This question is from textbook
: I need someone help I'm totally stuck. please please help. Thank you.
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

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
when D, which is the discriminant , is less than zero you will get complex roots
:
D=b%5E2-4ac and a,b,and c are coefficients of a standard quadratic equation
:
ax%5E2%2Bbx%2Bc=0The reason why D<0 is complex is because you are taking the square root of D.....so naturally a square root of a negative number will be complex.
:
x^2 + 5x + 7 = 0 would be and example
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%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=%285%29%5E2-4%2A1%2A7=-3.

The discriminant -3 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 -3 is + or - sqrt%28+3%29+=+1.73205080756888.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B7+%29