SOLUTION: What is the value of the discriminant of x^2-5x-14=0? A) 81 B) 31 C) -31 D) -81 I am not sure where to start on this? Can someone give me some direction? THANK YOU!

Algebra ->  Expressions-with-variables -> SOLUTION: What is the value of the discriminant of x^2-5x-14=0? A) 81 B) 31 C) -31 D) -81 I am not sure where to start on this? Can someone give me some direction? THANK YOU!       Log On


   

Question 28813: What is the value of the discriminant of x^2-5x-14=0?
A) 81
B) 31
C) -31
D) -81
I am not sure where to start on this? Can someone give me some direction? THANK YOU!
Answer by stanbon(75887) 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-5x%2B-14+=+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=%28-5%29%5E2-4%2A1%2A-14=81.

Discriminant d=81 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+81+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+81+%29%29%2F2%5C1+=+7
x%5B2%5D+=+%28-%28-5%29-sqrt%28+81+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B-5x%2B-14 can be factored:
1x%5E2%2B-5x%2B-14+=+1%28x-7%29%2A%28x--2%29
Again, the answer is: 7, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B-14+%29

Hope this helps.
Cheers,
Stan H.