SOLUTION: How do you know if a quadratic equation will have one, two, or no solutions? How do you find a quadratic equation if you are only given the solution? Is it possible to have differ

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Question 256064: How do you know if a quadratic equation will have one, two, or no solutions? How do you find a quadratic equation if you are only given the solution? Is it possible to have different quadratic equations with the same solution? Will you explain this to me, please?
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Look below at the discriminant.
if the discriminant is greater than zero there are two solutions
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=16 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3, -1. Here's your graph:


if the discriminant is zero there is one solution (or the same solution twice)
if the discriminant is less than zero there are no real solutions

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