SOLUTION: r-6r^2 =-1

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Question 24213: r-6r^2 =-1
Answer by Alwayscheerful(414) 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 -6r%5E2%2B1r%2B1+=+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=%281%29%5E2-4%2A-6%2A1=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+25+%29%29%2F2%5Ca.

r%5B1%5D+=+%28-%281%29%2Bsqrt%28+25+%29%29%2F2%5C-6+=+-0.333333333333333
r%5B2%5D+=+%28-%281%29-sqrt%28+25+%29%29%2F2%5C-6+=+0.5

Quadratic expression -6r%5E2%2B1r%2B1 can be factored:
-6r%5E2%2B1r%2B1+=+-6%28r--0.333333333333333%29%2A%28r-0.5%29
Again, the answer is: -0.333333333333333, 0.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-6%2Ax%5E2%2B1%2Ax%2B1+%29

Hope this helps!