please explain why finding roots of equation is important  TOPIC_SOLVED

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.

please explain why finding roots of equation is important

Postby prioris on Sat Jul 11, 2009 8:20 pm

i understand finding the roots of an equation as finding the X intercept.

so i am able to find a few points on the graph thru factoring the equation.

whoop dee doo!!!

from a practical point of view, that is still a meaningless abstraction for me and doesn't explain the practical use or explain why mathematicians and scientists find them so important.

can someone explain the deeper meaning of why finding the roots of an equation is so important.

i can digest a lot of other math abstractions but i have not found anything that explains ROOTS OF AN EQUATION in more simpler terms of why

thanks
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Postby stapel_eliz on Sun Jul 12, 2009 10:20 pm

When you're trying to find where two modelling equations intersect, where information overlaps, this is equilvalent to finding the zeroes of the difference of the models. For this, and many other reasons that you'll learn once you get to applications, algebra is foundational to much of science.
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Re: please explain why finding roots of equation is important

Postby prioris on Mon Jul 13, 2009 1:51 am

i still don't understand

you are saying that the main practical use is determining whether two or more equations intersect and that's it.

it still gives no deep understanding of the abstraction of f(x)=0 and the historical perspective on why so much focus on it.
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Postby stapel_eliz on Mon Jul 13, 2009 1:57 am

I don't know what you mean by "deep understanding"...? As for the practical applications, you'll need to enter the study of those practical topics to learn how the various tools are used.

Your question is akin to a child demanding to know the "deep meaning" of the alphabet, requiring to know all the ways that letters, etc, could possibly be used in a practical context, and all the history "justifying" their use throughout history, before consenting to learn his ABCs. The question is nearly unanswerable, and is not terribly relevant.

If you're wanting to know how scientists use this stuff, you might want to talk to some scientists. If you need to know how economists or engineers use this, then talk to them. If you want to learn the history of algebra, etc, then try studying some of the various books available on the topic. But math teachers generally just know the math, not the industry-specific stuff. We don't usually have the "real world" or "philosophical" information you seem to be wanting.

Sorry.
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Re: please explain why finding roots of equation is important  TOPIC_SOLVED

Postby Martingale on Mon Jul 13, 2009 3:09 am

prioris wrote:
you are saying that the main practical use is determining whether two or more equations intersect and that's it.



It's one of the uses... and it's a big one (you are underestimating the importance of this). There are also application in calculus (minimization/maximization) and Linear algebra (nullspace) though I'm not going to go into specifics.
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Re: please explain why finding roots of equation is important

Postby prioris on Tue Jul 14, 2009 7:14 pm

so roots don't really have any real deeper abstract meaning. it is what it is.

the essence of roots is just finding the x-intercept points and then utilizing that information to help at arriving at solutions or answering questions.

i just wanted to make sure i wasn't missing anything.

ok
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