SOLUTION: I must use the discriminant to determine the number of solutions of the quadratic equation and whether the solutions are real or complex. I am having trouble understanding how to f

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I must use the discriminant to determine the number of solutions of the quadratic equation and whether the solutions are real or complex. I am having trouble understanding how to f      Log On


   

Question 236090: I must use the discriminant to determine the number of solutions of the quadratic equation and whether the solutions are real or complex. I am having trouble understanding how to find the discriminant and then find the solutions.
I do not need to find the roots.
3z^2 + z - 1 = 0
Answer by philline_palana(20) 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 3z%5E2%2B1z%2B-1+=+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%2A3%2A-1=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%5C3+=+0.434258545910665
z%5B2%5D+=+%28-%281%29-sqrt%28+13+%29%29%2F2%5C3+=+-0.767591879243998

Quadratic expression 3z%5E2%2B1z%2B-1 can be factored:
3z%5E2%2B1z%2B-1+=+3%28z-0.434258545910665%29%2A%28z--0.767591879243998%29
Again, the answer is: 0.434258545910665, -0.767591879243998. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B1%2Ax%2B-1+%29