How do you write a rational equation given only the solutions?
An equation can be written given the solutions of the equation in the following way. Assume an equation f(x) = 0 has the roots x1 and x2.
The corresponding equation would be (x - x1)(x - x2) = 0
=> x^2 - (x1 + x2)*x + x1*x2 = 0
For a higher order equation with solutions x1, x2, x3..., the corresponding equation is (x - x1)(x - x2)(x - x3)... = 0. This can be simplified to give an equation in the standard form.
The same is applicable for the creation of an equation of any order.