How do you find a quadratic equation if you are only given the solution?
There are an infinite number of equations that will give the same answer, but they are not independent.
Quadratic equations have two solutions. Suppose they are a and b.
One equation with those two solutions is
(x-a)(x-b) = x^2 -(a+b)x + ab = 0
Any multiple of that equation will have the same solutions.