SOLUTION: 5b. What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x2 - 10x - 42 = 0." I appreciate your help, thank you.

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Question 182674: 5b.

What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x2 - 10x - 42 = 0."
I appreciate your help, thank you.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x2 - 10x - 42 = 0."
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This is well covered by the onsite solver.
As an example
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=529 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2.33333333333333, -1.5. Here's your graph:

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2 methods are covered, the quadratic equation and factoring. (The solver gets the factors wrong if the coeff of the x^2 is not 1.)
The 3rd method is completing the square. Once you know the quadratic equation, use it and forget about completing the square.
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Graphical solutions might be a 4th method.
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