Solving Quadratic Equations with Square Roots

Let's write the equation in the form $f(x)=a(x-p)(x-q).$ The leading coefficient $a$ can be any non-zero real number and $p$ and $q$ are the zeros of the function. Since the roots are $8$ and $12,$ our equation can be written as follows. $$\begin{array}{c}f(x)=a(x-8)(x-12)\end{array}$$ Note that any equation in the above form will have roots $8$ and $11,$ regardless the value of $a.$ For simplicity, let's set $a=1.$ Note that there are infinitely many equations that satisfy the given condition. This is just one of them.