SOLUTION: please help ! z^2+z-3

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Question 19317: please help !
z^2+z-3
Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation az%5E2%2Bbz%2Bc=0 (in our case 1z%5E2%2B1z%2B-3+=+0) has the following solutons:

z%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=%281%29%5E2-4%2A1%2A-3=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+13+%29%29%2F2%5Ca.

z%5B1%5D+=+%28-%281%29%2Bsqrt%28+13+%29%29%2F2%5C1+=+1.30277563773199
z%5B2%5D+=+%28-%281%29-sqrt%28+13+%29%29%2F2%5C1+=+-2.30277563773199

Quadratic expression 1z%5E2%2B1z%2B-3 can be factored:
1z%5E2%2B1z%2B-3+=+1%28z-1.30277563773199%29%2A%28z--2.30277563773199%29
Again, the answer is: 1.30277563773199, -2.30277563773199. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-3+%29

Hope this helps!