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 ->  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

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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(12) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=13 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.434258545910665, -0.767591879243998. Here's your graph: