SOLUTION: Please help me calculate the value of the discriminant of {{{x^2+x+3=0}}} and part b of that question is By examining the sign of the discriminant in part a, how many x-intercepts

Algebra ->  Linear-equations -> SOLUTION: Please help me calculate the value of the discriminant of {{{x^2+x+3=0}}} and part b of that question is By examining the sign of the discriminant in part a, how many x-intercepts       Log On


   

Question 148151: Please help me calculate the value of the discriminant of x%5E2%2Bx%2B3=0 and part b of that question is By examining the sign of the discriminant in part a, how many x-intercepts would the graph of y=x%5E2%2Bx%2B3 have? and why?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B3+=+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=%281%29%5E2-4%2A1%2A3=-11.

The discriminant -11 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 -11 is + or - sqrt%28+11%29+=+3.3166247903554.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B3+%29

As noted above and shown in the graph, there are NO x intercepts. This is true when the discriminant is negative.