Forming Quadratic Equations

1. Finding a Quadratic Equation
1. If the roots of the quadratic equation are and , and the coefficient of is :
   
   This expands to:
   
2. If the quadratic equation has a double root (repeated root) , and the coefficient of is :
   


2. Roots of a Quadratic Equation with Rational Coefficients
   If the quadratic equation (where are rational numbers) has one root in the form , the other root will be , where and are rational numbers and is an irrational number.