How many ways are there to solve a quadratic equation? - Answers

There are so far 8 common methods to solve quadratic equations:GraphingFactoring FOIL methodCompleting the square.Using the quadratic formula (derived from algebraic manipulation of "completing the square" method).The Diagonal Sum Method. It quickly and directly gives the 2 real roots in the form of 2 fractions. In fact, it can be considered as a shortcut of the factoring method. It uses the Rule of Signs for Real Roots in its solving process. When a= 1, it can give the 2 real roots quickly without factoring. Example. Solve x^2 - 39x + 108 = 0. The Rule of Signs indicates the 2 real roots are both positive. Write the factor-sets of c = 108. They are: (1, 108), (2, 54), (3, 36)...Stop! This sum is 36 + 3 = 39 = -b. The 2 real roots are 3 and 36. No needs for factoring! When a is not one, this new method selects all probable root-pairs, in the form of 2 fractions. Then it applies a very simple formula to see which root-pair is the answer. Usually, it requires less than 3 trials. If this new method fails, then this given quadratic equation can not be factored, and consequently the quadratic formula must be used. Please see book titled:"New methods for solving quadratic equations and inequalities" (Amazon e-book 2010).The Bluma MethodThe factoring AC Method (YouTube). This method is considerably improved by a "new and improved AC Method", recently introduced on Google or Yahoo Search.The new Transforming Method, recently introduced, that is may be the best and fastest method to solve quadratic equations. Its strong points are: simple, fast, systematic, no guessing, no factoring by grouping, and no solving the binomials. To know this new method, read the articles titled:"Solving quadratic equations by the new Transforming Method" on Google or Yahoo Search.BEST METHODS TO SOLVE QUADRATIC EQUATIONS. A. When the equation can't be factored, the best choice would be the quadratic formula. How to know if the equation can't be factored? There are 2 ways:1. Start solving by the new Transforming Method in composing factor pairs of a*c (or c). If you can't find the pair whose sum equals to (-b), or b, then the equation can't be factored.2. Calculate the Discriminant D = b^2 - 4ac. If D isn't a perfect square, then the equation can't be factored.B. When the equation can be factored, the new Transforming Method would be the best choice.