SOLUTION: I need help with these questions! I did the other 20 but these are too hard! 1) 3r^2-16r-7=0

Algebra ->  Test -> SOLUTION: I need help with these questions! I did the other 20 but these are too hard! 1) 3r^2-16r-7=0       Log On


   

Question 713847: I need help with these questions! I did the other 20 but these are too hard!
1) 3r^2-16r-7=0
Answer by BGutridge(15) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ar%5E2%2Bbr%2Bc=0 (in our case 3r%5E2%2B-16r%2B-7+=+0) has the following solutons:

r%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=%28-16%29%5E2-4%2A3%2A-7=340.

Discriminant d=340 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+340+%29%29%2F2%5Ca.

r%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+340+%29%29%2F2%5C3+=+5.73984815243096
r%5B2%5D+=+%28-%28-16%29-sqrt%28+340+%29%29%2F2%5C3+=+-0.406514819097629

Quadratic expression 3r%5E2%2B-16r%2B-7 can be factored:
3r%5E2%2B-16r%2B-7+=+3%28r-5.73984815243096%29%2A%28r--0.406514819097629%29
Again, the answer is: 5.73984815243096, -0.406514819097629. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-16%2Ax%2B-7+%29