SOLUTION: 5b^3+34b^2=7b

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Question 38525This question is from textbook
: 5b^3+34b^2=7b This question is from textbook

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
5b%5E3%2B34b%5E2=7b
5b%5E3%2B34b%5E2-7b=0
b%285b%5E2%2B34b-7%29=0
b=0 and 'b' equals the two values below.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B34x%2B-7+=+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=%2834%29%5E2-4%2A5%2A-7=1296.

Discriminant d=1296 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-34%2B-sqrt%28+1296+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2834%29%2Bsqrt%28+1296+%29%29%2F2%5C5+=+0.2
x%5B2%5D+=+%28-%2834%29-sqrt%28+1296+%29%29%2F2%5C5+=+-7

Quadratic expression 5x%5E2%2B34x%2B-7 can be factored:
5x%5E2%2B34x%2B-7+=+5%28x-0.2%29%2A%28x--7%29
Again, the answer is: 0.2, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B34%2Ax%2B-7+%29