We’ve all done the homework work before in a Calculus class but are any of our answers, giving us the most useful results? Most students always ask: are any of my Solving Quadratic Equations Using Different Methods Worksheet Answers better than the other ones?
There are two main approaches to solving a quadratic equation. One is to work from the points of integration and the other is to use the middle term in the quadratic equation. Both have their strengths and weaknesses, and knowing this will help you choose the right method for your particular problem.
An important point to note is that even if you find the solution using the middle term method, you should still always know how to integrate by hand. The reason is that it can be very easy to forget what the result is, and a wrong integration can give you more errors than the right one. Also, by only integrating by hand, you can still get a good approximation when working with large and/or complex variables. This also means that it is much harder to find solutions using a numerical method than it is to find them with a hand-written integration.
How can you tell which method is better for you? While a hand-written method can get you the most effective solution, its time-consuming nature may be too much for some students. To avoid wasting valuable time on tedious methods, try and solve the quadratic equation as quickly as possible.
If the quadratic equation is large, it may also take a long time to solve. Since this is a long-term solution for a short-term problem, a fast way to solve it would be to use a method that gets a faster result the longer it goes on. What I mean by this is that a numerical method may be very useful for solving integrals but for short-term integrals, using an integral only takes a couple of minutes. It’s better to do a longer integrand first and then go for the smaller integral.
If you are not sure which method is best for you, you should try both methods until you get a solution that you are satisfied with. Look at how many times you go back and forth between methods and which way you feel is more efficient. The obvious method for both cases is to try to find the best method that gives you the most accurate results and then stick with it. Once you find this, you can switch between different methods depending on the complexity of the problem.
Since this is a two-step process, the hand-written method may get faster over time because you are learning how to integrate by hand while getting better results from it. Also, if you are doing long integrals, you can be quite comfortable just doing integrals by hand with a reliable program like Matlab, because there is no need to take the time to manually lookup tables or figure out how to integrate.
If you cannot or do not want to stick with a hand-written method, you should learn to integrate by hand. While the results will be less accurate, it will also take a lot less time and work so you will be more productive.