SOLUTION: Give exact and approximate solutions to three decimal places. x^2-5x+3=0 The exact solutions are x=__? (use radicals as needed. Use commas to separate answers) The approxim

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Give exact and approximate solutions to three decimal places. x^2-5x+3=0 The exact solutions are x=__? (use radicals as needed. Use commas to separate answers) The approxim      Log On


   

Question 330877: Give exact and approximate solutions to three decimal places.
x^2-5x+3=0
The exact solutions are x=__?
(use radicals as needed. Use commas to separate answers)
The approximate solutions to three decimal places are x=___?
(use a comma to separate answers)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Give exact and approximate solutions to three decimal places.
x^2-5x+3=0
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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-5x%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=%28-5%29%5E2-4%2A1%2A3=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+13+%29%29%2F2%5C1+=+4.30277563773199
x%5B2%5D+=+%28-%28-5%29-sqrt%28+13+%29%29%2F2%5C1+=+0.697224362268005

Quadratic expression 1x%5E2%2B-5x%2B3 can be factored:
1x%5E2%2B-5x%2B3+=+%28x-4.30277563773199%29%2A%28x-0.697224362268005%29
Again, the answer is: 4.30277563773199, 0.697224362268005. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B3+%29

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This below is a waste of your time and mine.
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The exact solutions are x=__?
(use radicals as needed. Use commas to separate answers)
The approximate solutions to three decimal places are x=___?
(use a comma to separate answers)