SOLUTION: Find all intercepts for the graph of the quadratic function. f(x) = 5x2 – 38x + 21

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Question 471511: Find all intercepts for the graph of the quadratic function.
f(x) = 5x2 – 38x + 21
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
5x2-38x+21=0
(5x-3)(x-7)=0
x=3/5 or 7
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-38x%2B21+=+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=%28-38%29%5E2-4%2A5%2A21=1024.

Discriminant d=1024 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--38%2B-sqrt%28+1024+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-38%29%2Bsqrt%28+1024+%29%29%2F2%5C5+=+7
x%5B2%5D+=+%28-%28-38%29-sqrt%28+1024+%29%29%2F2%5C5+=+0.6

Quadratic expression 5x%5E2%2B-38x%2B21 can be factored:
5x%5E2%2B-38x%2B21+=+5%28x-7%29%2A%28x-0.6%29
Again, the answer is: 7, 0.6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-38%2Ax%2B21+%29
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