SOLUTION: for the following equation, state the value of the discriminant and then describve the nature of the solution -8x^2+5x+13=0

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Question 446744: for the following equation, state the value of the discriminant and then describve the nature of the solution -8x^2+5x+13=0
Answer by chriswen(106) 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 -8x%5E2%2B5x%2B13+=+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=%285%29%5E2-4%2A-8%2A13=441.

Discriminant d=441 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+441+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+441+%29%29%2F2%5C-8+=+-1
x%5B2%5D+=+%28-%285%29-sqrt%28+441+%29%29%2F2%5C-8+=+1.625

Quadratic expression -8x%5E2%2B5x%2B13 can be factored:
-8x%5E2%2B5x%2B13+=+-8%28x--1%29%2A%28x-1.625%29
Again, the answer is: -1, 1.625. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-8%2Ax%5E2%2B5%2Ax%2B13+%29