What are two algebraic methods for solving quadratic equations?

Answer 1

Finally, there are two methods to use, depending on if the given quadratic equation can be factored or not.

1.- The first one is the new Diagonal Sum Method, recently presented in book titled: "New methods for solving quadratic equations" (Trafford 2009). This method directly gives the two roots in the form of two fractions, without having to factor it. The innovative concept of this new method is finding 2 fractions knowing their product (c/a) and their sum (-b/a). This new method is applicable to any quadratic equation that can be factored. It can replace the existing trial-and-error factoring method since this last one contains too many more permutations. In general, it is hard to tell in advance if a given quadratic equation can be factored. However, if the new method fails to get the answers, then you can positively conclude that this equation can not be factored. Consequently, the quadratic formula must be used in solving. We advise students to always try to solve the given equation by the new method first.

If the student gets conversant with this method, it usually take less than 2 trials to get answers.

2. the second one uses the quadratic formula that students can find in any algebra book. This formula must be used for all quadratic equations that can not be factored.