SOLUTION: How do I find the roots of y=x^2-8x+7 by factoring and also by using the quadratic equation?

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Question 332521: How do I find the roots of y=x^2-8x+7 by factoring and also by using the quadratic equation?
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E2-8x%2B7
Equate to zero:
x%5E2-8x%2B7=0
What factors of 7 can be combined to add up to -8?
How about -7 an -1?
%28x-7%29%28x-1%29=0
Equate each term to zero and solve for x:
highlight%28x=7%29
highlight%28x=1%29
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B7+=+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=%28-8%29%5E2-4%2A1%2A7=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+36+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+36+%29%29%2F2%5C1+=+7
x%5B2%5D+=+%28-%28-8%29-sqrt%28+36+%29%29%2F2%5C1+=+1

Quadratic expression 1x%5E2%2B-8x%2B7 can be factored:
1x%5E2%2B-8x%2B7+=+1%28x-7%29%2A%28x-1%29
Again, the answer is: 7, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B7+%29