SOLUTION: The equation 4x^2+15x+2=0 has two solutions A and B where A less than B and A= B=

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Question 425058: The equation 4x^2+15x+2=0 has two solutions A and B where A less than B
and A=
B=
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B15x%2B2+=+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=%2815%29%5E2-4%2A4%2A2=193.

Discriminant d=193 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-15%2B-sqrt%28+193+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2815%29%2Bsqrt%28+193+%29%29%2F2%5C4+=+-0.138444501318775
x%5B2%5D+=+%28-%2815%29-sqrt%28+193+%29%29%2F2%5C4+=+-3.61155549868123

Quadratic expression 4x%5E2%2B15x%2B2 can be factored:
4x%5E2%2B15x%2B2+=+%28x--0.138444501318775%29%2A%28x--3.61155549868123%29
Again, the answer is: -0.138444501318775, -3.61155549868123. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B15%2Ax%2B2+%29

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