Solving quadratic equations with continued fractions

In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is where a ≠ 0. The quadratic equation can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated as a decimal fraction only by applying an additional root extraction algorithm. If the roots are real, there is an alternative technique that obtains a rational approximation to one of the roots by manipulating the equation directly. The method works in many cases, and long ago it stimulated further development of the analytical theory of continued fractions.