SOLUTION: If I have a solution how can I create a quadric equation

Question 372140: If I have a solution how can I create a quadric equation
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You can't, in general. That is because you need two solutions to create a quadratic. However, in some cases, the character of the solution that you do have allows you to deduce the solution that you don't have.

For example, if you have a solution that looks like

Then, because of symmetry, the other solution is guaranteed to be:

.

Likewise, if you have a single complex number solution, then the other solution is the conjugate of that complex number.

On the other hand, if you only have one rational number solution, you are at a dead end, unless you know that your single rational solution has a multiplicity of two.

Given that you do have two solutions, let's call them

and

, all you have to do is calculate the product:

And set that product equal to zero.
In the case where you have one solution with a multiplicity of two, meaning you have two identical solutions, you can calculate:

John

My calculator said it, I believe it, that settles it

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