Find quadratic equation who's roots are 1/2 and -1/3

Let's say you have the factored quadratic (x-5)^2=0. The root is just 5, because when you set x-5 to zero and solve for x you have 5. In the same way, we can factor the equation as (x-1/2)(x+1/3), because if you set x-1/2=0 the solution is 1/2. The x+1/3 can also be set to zero and you get -1/3 . Therefore the quadratic has to be (x-1/2)(x+1/3).Foiling this out you get x^2-1/6x-1/6. Note we have to set this equal to zero like the first equation, so the answer is x^2-1/6x-1/6=0

step-by-step explanation: