Consider the general quadratic equation:
           where

Multiply to create a leading coefficient of 1:
              

Represent the roots of the equation as  and:
               

Comparing the equations, it can be seen that:
         or     

and       

Sum of the roots:

Product of the roots:

Therefore, the formula for the sum of roots is

And the formula for the product of roots is

Example: roots are -3 and .

The sum of the roots is.
   So the coefficient of the second term will be (the negation of the sum).

The product of the roots is.

So the constant term will be.