SOLUTION: what is the trinomial function for 4a squared plus 9a plus 20.25 equals 21.25?

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Question 270102: what is the trinomial function for 4a squared plus 9a plus 20.25 equals 21.25?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
4a^2+9a+20.25=21.25
4a^2+9a-1=0
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B9x%2B-1+=+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=%289%29%5E2-4%2A4%2A-1=97.

Discriminant d=97 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+97+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%289%29%2Bsqrt%28+97+%29%29%2F2%5C4+=+0.106107225224513
x%5B2%5D+=+%28-%289%29-sqrt%28+97+%29%29%2F2%5C4+=+-2.35610722522451

Quadratic expression 4x%5E2%2B9x%2B-1 can be factored:
4x%5E2%2B9x%2B-1+=+4%28x-0.106107225224513%29%2A%28x--2.35610722522451%29
Again, the answer is: 0.106107225224513, -2.35610722522451. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B9%2Ax%2B-1+%29