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anonymous
 one year ago
How could you use Descartes' rule and the Fundamental Theorem of Algebra to predict the number of complex roots to a polynomial as well as find the number of possible positive and negative real roots to a polynomial?
anonymous
 one year ago
How could you use Descartes' rule and the Fundamental Theorem of Algebra to predict the number of complex roots to a polynomial as well as find the number of possible positive and negative real roots to a polynomial?

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.1What is Descartes' rule?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0possible number of the positive roots of a polynomial is equal to the number of sign changes in the coefficients of the terms or less than the sign changes by a multiple of 2.

LynFran
 one year ago
Best ResponseYou've already chosen the best response.0http://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.764641.html

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1You don't understand it, right?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1let's look at example: \(x^5x^4+x+2=0\) how many time the sign of the term change?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1ok!! what is the sign of x^5?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1what is the sign of x^4 ?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1yes, so, if you go from x^5 to x^4 the sign changes from + to , right? one time!!

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1now, next , what is the sign of x ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Got it! Basically the number of signs changes is the number of possible roots, correct?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1OK, tell me, on the expression above, how many time the sign change in total?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1yup, so the POSSIBLE real roots are ???

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So this is the Descartes rule?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How come it's either 0?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1that is the rule, if the number of the changing of the sign is 6, then the number of real root can be 6,4,2,0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0multiple of 2, right?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1What is the degree of the expression above?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1yup, so the number of real root are 2 (maximum), hence the maximum of complex is ??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Are we now talking about the Fundamental Theorem of Algebra?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay. :) So in the Fundamental Theorem of Algebra, it's about the complex numbers?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so the equation above has a degree of 5.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i already answered that lol

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1degree 5> maximum 5 roots, we already know that it MAY have 2 real roots, hence, how many complex left?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and 2 complex roots, since the real roots are 2

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1perfect!! but confirm: why 2 but 3??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because complex roots are always in pairs?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1yyyyyyyyyyyyyyyyyyyyyyyyyyyyyes!

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1go to bed!! we are done.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wow, i didn't know that that's easy. thank you @Loser66 ! :) You're a great help!
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