SOLUTION: Find the value of r in the quadratic equation: r (to the 2nd power) - 7r - 8 = 0.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the value of r in the quadratic equation: r (to the 2nd power) - 7r - 8 = 0.       Log On


   

Question 82034: Find the value of r in the quadratic equation:
r (to the 2nd power) - 7r - 8 = 0.
Answer by jim_thompson5910(35256) 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 1r%5E2%2B-7r%2B-8+=+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=%28-7%29%5E2-4%2A1%2A-8=81.

Discriminant d=81 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+81+%29%29%2F2%5Ca.

r%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+81+%29%29%2F2%5C1+=+8
r%5B2%5D+=+%28-%28-7%29-sqrt%28+81+%29%29%2F2%5C1+=+-1

Quadratic expression 1r%5E2%2B-7r%2B-8 can be factored:
1r%5E2%2B-7r%2B-8+=+1%28r-8%29%2A%28r--1%29
Again, the answer is: 8, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B-8+%29