SOLUTION: I am a parent trying to help my student and she has to show her work. f(x)=x to the second power -8x+3 Approximate the zeros of the functi

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Question 733508: I am a parent trying to help my student and she has to show her work. f(x)=x to the second power -8x+3
Approximate the zeros of the function to the nearest tenth.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=x^2 - 8x + 3
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B3+=+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%2A3=52.

Discriminant d=52 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+52+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+52+%29%29%2F2%5C1+=+7.60555127546399
x%5B2%5D+=+%28-%28-8%29-sqrt%28+52+%29%29%2F2%5C1+=+0.394448724536011

Quadratic expression 1x%5E2%2B-8x%2B3 can be factored:
1x%5E2%2B-8x%2B3+=+%28x-7.60555127546399%29%2A%28x-0.394448724536011%29
Again, the answer is: 7.60555127546399, 0.394448724536011. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B3+%29

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