SOLUTION: Find the discriminant for each equation. Describe the roots. Give D, then the number of rational, irrational or complex roots. ( ex: 36, 2 rational) x^2-x +6=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the discriminant for each equation. Describe the roots. Give D, then the number of rational, irrational or complex roots. ( ex: 36, 2 rational) x^2-x +6=0      Log On


   

Question 627758: Find the discriminant for each equation. Describe the roots.
Give D, then the number of rational, irrational or complex roots. ( ex: 36, 2 rational)
x^2-x +6=0
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B6+=+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=%28-1%29%5E2-4%2A1%2A6=-23.

The discriminant -23 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 -23 is + or - sqrt%28+23%29+=+4.79583152331272.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B6+%29