SOLUTION: how do i find all real or imaginary solutions? 3v^2+4v-1=0

Question 182866: how do i find all real or imaginary solutions?
3v^2+4v-1=0
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
how do i find all real or imaginary solutions?
3v^2+4v-1=0
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Same as always, using the quadratic equation.

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=28 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.21525043702153, -1.54858377035486. Here's your graph:

The onsite solver's opinion of factoring is a bit loose, and if the coefficient of the x^2 term is not 1, you have to make some adjustments.
Also, it defaults to x for the variable.

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