![]() ![]() Then this strategy would have worked assuming that there are some solutions. In fact, it would have worked if you did not have Now, there's some cases in which this strategy would have worked. You still don't know what x is, and it's really not clear what to do with this algebraically. Of negative four x minus four, but this still doesn't help you. And you could get something like this, you would get x is equal to plus or minus the square root The plus of minus of one side to make sure you're Square root of x squared is equal to, and you could try to take ![]() And now, someone might say, if I take the square root of both sides, I could get, I'll just write that down. And then what happens? On the left hand side, you do indeed isolate the x squared, and on the right hand side, you get negative four x minus four. Isolate that x squared by subtracting four x from both sides and subtracting three from both sides. So you could imagine, let me just rewrite it. People will try to go for is to isolate the x squared first. So just willy nilly, taking the square root ofīoth sides of a quadratic is not going to be too helpful. Isolate the x over here? You've pretty quickly hit a dead end. But even if this wasĪ positive value here, how do you simplify or how do you somehow Even if this wasn't a negative one here, that's the most obvious problem. Plus four x plus three is equal to the square The square root of both sides? And if you did that, you would get the square root of x squared So one strategy that people might try is, well, I have something squared, why don't I just try to take I have something on both sides of an equal sign. Why is it a quadratic equation? Well, it's a quadratic because it has this secondĭegree term right over here and it's an equation because 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.- In this video, we're gonna talk aboutĪ few of the pitfalls that someone might encounter while they're trying to solve a quadratic equation like this. 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. In ancient times, mathematicians were interested in solving such problems geometrically. Pattern recognition of perfect square trinomials.Guessing (perhaps helped by rational roots theorem).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. 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. This formula is easier to remember and to compute as compared to the classic 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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