SOLUTION: For the following equation, state the value of the discriminant and then describe the nature of the solutions. -4x^2+4x+7=0 What is the value of the discriminant?

Algebra ->  Real-numbers -> SOLUTION: For the following equation, state the value of the discriminant and then describe the nature of the solutions. -4x^2+4x+7=0 What is the value of the discriminant?      Log On


   

Question 265802: For the following equation, state the value of the discriminant and then describe the nature of the solutions.
-4x^2+4x+7=0
What is the value of the discriminant?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The on-site solver covers this well.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4x%5E2%2B4x%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=%284%29%5E2-4%2A-4%2A7=128.

Discriminant d=128 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+128+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+128+%29%29%2F2%5C-4+=+-0.914213562373095
x%5B2%5D+=+%28-%284%29-sqrt%28+128+%29%29%2F2%5C-4+=+1.9142135623731

Quadratic expression -4x%5E2%2B4x%2B7 can be factored:
-4x%5E2%2B4x%2B7+=+%28x--0.914213562373095%29%2A%28x-1.9142135623731%29
Again, the answer is: -0.914213562373095, 1.9142135623731. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4%2Ax%5E2%2B4%2Ax%2B7+%29