SOLUTION: Evaluate all rational roots for X^2+3X-17.

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Question 923761: Evaluate all rational roots for X^2+3X-17.
Found 2 solutions by josgarithmetic, ewatrrr:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
RATIONAL! Try factoring... but 17 & 1 will not give your linear coefficient.

Try looking at discriminant:
%283%29%5E2-4%2A1%2A%28-17%29=9%2B68=77

Two IRRATIONAL roots, if you want them.
X=%28-3%2B-+sqrt%2877%29%29%2F2

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
X^2+3X-17 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-17+=+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=%283%29%5E2-4%2A1%2A-17=77.

Discriminant d=77 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+77+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+77+%29%29%2F2%5C1+=+2.88748219369606
x%5B2%5D+=+%28-%283%29-sqrt%28+77+%29%29%2F2%5C1+=+-5.88748219369606

Quadratic expression 1x%5E2%2B3x%2B-17 can be factored:
1x%5E2%2B3x%2B-17+=+1%28x-2.88748219369606%29%2A%28x--5.88748219369606%29
Again, the answer is: 2.88748219369606, -5.88748219369606. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-17+%29