It seems that in general it is easier to use one of the standard methods, then convert that to a continued fraction, but there are some special cases that do have straightforward direct continued fraction solutions. I was curious as to whether there was a direct way to express the solution of a general quadratic equation as a continued fraction. Note that it is also possible to solve cubic equations geometrically, but only if you use a less favoured construction called "neusis" which requires a marked straight edge (or if you use origami). You can solve quadratic equations directly using straight edge and compass constructions. Therefore, students are advised to use it as their go-to technique whenever they must solve a quadratic equation. We found that the new method, 4, was the fastest, easiest to remember, and easiest to perform. There are so far 8 common methods to solve quadratic equations, They are: graphing, completing the squares, quadratic formula, factoring FOIL, The Diagonal Sum Method, the Bluma Method, the popular factoring AC Method, and the new Transforming Method. We have compared four methods for solving quadratic equations, three traditional ones, and a new one. If the quadratic equation is of the form ax + bx + c 0, where a 0 and the quadratic expression is not factorable, try completing the square. When solving quadratic equations in general, first get everything over onto one side of the equals sign (something that was already done in the above examples). In ancient times, mathematicians were interested in solving such problems geometrically. Best method to solve quadratic equations. Pattern recognition of perfect square trinomials.Guessing (perhaps helped by rational roots theorem).Factorisation: The first step for factorisation is to see if a common factor can be taken out. The answer "As many as you like" may sound frivolous, but there are many ways to solve them and you may want to make your own for a particular circumstance. What are the different methods of solving quadratic equations 1. No factoring by grouping and no solving binomials!!! Proceeding: find 2 real roots of f'(x), then, divide them by a = 8.įind 2 real roots knowing the sum(-b = 22), and the product (ac= -104). It helps avoid the lengthy factoring by grouping and the solving of the 2 binomials.Įxample. When f(x) can be factored, the new Transforming Method (Google) may be the best method to perform. 4) Determine the number of solutions using the discriminant. This formula is easier to remember and to compute as compared to the classic formula. 3) Solve a quadratic with quadratic formula. However, there is an improved quadratic formula in graphic form (Google) that is interesting to know. the quadratic formula is the obvious choice. When the quadratic equation f(x) = 0 can't be factored. The popular factoring AC method, and the new Transforming Method (Socratic, Google Search) Graphing, completing the square, factoring FOIL, quadratic formula, So far, there are 6 methods to solve quadratic functions.
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