How do you find a quadratic equation if you are only given the solution?

Answer 1

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.