SOLUTION: Write a quadratic equation having the given numbers as solutions. -3.5, 2.2

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Question 281364: Write a quadratic equation having the given numbers as solutions. -3.5, 2.2
Found 2 solutions by oberobic, graphmatics:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The general form of a quadratic equation that has been solved is to have two factors that are multiplied. In this case, you're told the solutions are x= -3.5 and x=2.2. So the factored form of the equation would be:
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(x + 3.5)(x - 2.2) = 0
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Using FOIL...
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x^2 -2.2x +3.5x -7.7 = 0
x^2 + 1.3x - 7.7 = 0
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multiply by 10 to get rid of the decimals...
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10x^2 + 13x - 77 = 0
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Checking this equation using the quadratic formula, you can determine if the solutions are x= -3.5 and x= 2.2...
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 10x%5E2%2B13x%2B-77+=+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=%2813%29%5E2-4%2A10%2A-77=3249.

Discriminant d=3249 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-13%2B-sqrt%28+3249+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2813%29%2Bsqrt%28+3249+%29%29%2F2%5C10+=+2.2
x%5B2%5D+=+%28-%2813%29-sqrt%28+3249+%29%29%2F2%5C10+=+-3.5

Quadratic expression 10x%5E2%2B13x%2B-77 can be factored:
10x%5E2%2B13x%2B-77+=+10%28x-2.2%29%2A%28x--3.5%29
Again, the answer is: 2.2, -3.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B13%2Ax%2B-77+%29

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Done

Answer by graphmatics(170) About Me  (Show Source):
You can put this solution on YOUR website!
(x+3.5)(x-2.2)
x**2+3.5x-2.2x-7.7
x**21.1x-7.7