SOLUTION: finding possible rational roots, listing rational roots I know how to find the possible rational zeros for each function but i dont know how to do the second step which is to find

Algebra ->  Rational-functions -> SOLUTION: finding possible rational roots, listing rational roots I know how to find the possible rational zeros for each function but i dont know how to do the second step which is to find      Log On


   

Question 867164: finding possible rational roots, listing rational roots
I know how to find the possible rational zeros for each function but i dont know how to do the second step which is to find all rational zeros
f(x)=2x^2-x-2
I know that the possible rational zeros are +-1, +-2 +-1/2
I would appreaciate any help. Thanks.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
quadratic EQ ALWAYS works
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-1x%2B-2+=+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=%28-1%29%5E2-4%2A2%2A-2=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+17+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+17+%29%29%2F2%5C2+=+1.28077640640442
x%5B2%5D+=+%28-%28-1%29-sqrt%28+17+%29%29%2F2%5C2+=+-0.780776406404415

Quadratic expression 2x%5E2%2B-1x%2B-2 can be factored:
2x%5E2%2B-1x%2B-2+=+2%28x-1.28077640640442%29%2A%28x--0.780776406404415%29
Again, the answer is: 1.28077640640442, -0.780776406404415. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-1%2Ax%2B-2+%29