SOLUTION: Determine the roots of the following quadratic equation x^2 - 14x + 45 = 0

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Question 36475: Determine the roots of the following quadratic equation
x^2 - 14x + 45 = 0
Answer by vidhyak(98) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-14x%2B45+=+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=%28-14%29%5E2-4%2A1%2A45=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--14%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+9
x%5B2%5D+=+%28-%28-14%29-sqrt%28+16+%29%29%2F2%5C1+=+5

Quadratic expression 1x%5E2%2B-14x%2B45 can be factored:
1x%5E2%2B-14x%2B45+=+1%28x-9%29%2A%28x-5%29
Again, the answer is: 9, 5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-14%2Ax%2B45+%29