SOLUTION: find the discriminant of 2x^2 + 9 = 4x and describe the nature of the roots of the equation. A)56; exactly one real root B)56; two distinct real roots C)-56; no real roots

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: find the discriminant of 2x^2 + 9 = 4x and describe the nature of the roots of the equation. A)56; exactly one real root B)56; two distinct real roots C)-56; no real roots      Log On


   

Question 209052: find the discriminant of 2x^2 + 9 = 4x and describe the nature of the roots of the equation.
A)56; exactly one real root
B)56; two distinct real roots
C)-56; no real roots
D)-56; two distinct real roots
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find the discriminant of 2x^2 + 9 = 4x and describe the nature of the roots of the equation.
A)56; exactly one real root
B)56; two distinct real roots
C)-56; no real roots
D)-56; two distinct real roots
--------------
This is covered well by the onsite solver.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-4x%2B9+=+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%2A2%2A9=-56.

The discriminant -56 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 -56 is + or - sqrt%28+56%29+=+7.48331477354788.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-4%2Ax%2B9+%29

-----------
Discriminant = -56 --> no real roots