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amistre64
 5 years ago
i learnt the other day that higher degree functions can always be reduced to linear and irreducible quadratic parts... but how to state that into a question, hmmm.......
amistre64
 5 years ago
i learnt the other day that higher degree functions can always be reduced to linear and irreducible quadratic parts... but how to state that into a question, hmmm.......

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nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.3The fundamental theorem of algebra states that in complex numbers any polynomial can be written as a product of linear parts. So because for polynomials with real coefficients alongside each root it's complex conjugate is a root too, those two linear parts \[xx_0\;\text{and}\; x\overline{x_0}\] will yield a quadratic part.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, thats what my teacher told me lol; I was like: thers a fundamental theorum of algebra? lol

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.3and the funny thing is, that mostly it is proven using analytic methods

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0can you decompose fraction into complex parts without messing things up in the end?

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.3I don't know what kind of a decomposition you are talking about, can you give an example?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{10x + 7}{(x1)(x^2+4)}\] for example..

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.3Do you mean real and imaginary part?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0imaginary parts; can this be decomposed into imaginary parts and not mess with the real solutions?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0and not mess up the reals lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the quad is irreducible unless you use imaginaries; and I was curious if we could break it down to all linear stuff

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i mean I guess I could take the time to actually do it, but then id have to get a pencil out and find some paper and ....its just alot of work :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I was surprised to find earlier this year that there was a fundamental theorem of arithmetic.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0wha!? arithmetics gone fundamental too?

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.3Oh yeah, that is correct. And because the real numbers are embedded into the complex, that won't change anything about the solutions. In fact the solution formula for higher dimensional polynomials are mostly written with complex numbers in mind. So you would get. \[x^2+4 = (x+4i)(x4i)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh amistre isnt that partial fraction decomposition?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yes it is; yes it is ;)

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.3ähm, sorry should be 2s instead of the 4s there ;)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0they are imaginary 4s lol..so it doesnt matter ;)
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