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July 5th, 2013, 11:14 AM   #31
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Re: Algebra/Polynomials

Quote:
 Originally Posted by Dacu Why accomplices solving problems?
If I understand you correctly, then perhaps you are asking whether you are being asked question when the original problem is already being solved, right? Well, you were the one to claim this :

Quote:
 Originally Posted by Dacu I believe that it is sufficient to know Fundamental Theorem Of Algebra and other theorems about the type of roots of equations with integer coefficients.
And you have to surely justify it, no? If you don't want to, may I assume it is false then?

 July 5th, 2013, 09:17 PM #32 Senior Member   Joined: Apr 2013 Posts: 425 Thanks: 24 Re: Algebra/Polynomials Hello,[color=#00BF00]mathbalarka[/color] If a polynomial equation of degree $n$ has only complex root $2 + 3i$ then how many real roots does that equation?Quote:"The theorem (in this case the fundamental theorem of algebra) is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly $n$ roots.". Wait and other opinions. Thank You!
July 5th, 2013, 09:28 PM   #33
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Re: Algebra/Polynomials

Quote:
 Originally Posted by Dacu If a polynomial equation of degree n has only 2 + 3i complex root then how many real roots does that equation?
I'd guess 0 if the polynomial is over R[x], but what this has to do with the question I asked? You're getting off the point.

Quote:
 Originally Posted by Dacu Quote:"The theorem (in this case the fundamental theorem of algebra) is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n roots."
Yes, this is FTA, but I can't relate this definition to that of the yours :

Quote:
 Originally Posted by Dacu any polynomial equation of degree n has n roots where n is integer
Which is clearly not true, no?

Quote:
 Originally Posted by Dacu Wait and other opinions.
You mean other's opinion? Anyone who knows a little bit of theory of equation would agree with me that FTA doesn't tell what you have said above and which is, in fact, false.

 July 5th, 2013, 09:34 PM #34 Senior Member   Joined: Apr 2013 Posts: 425 Thanks: 24 Re: Algebra/Polynomials [color=#00BF00]mathbalarka[/color], I have proposed a solution to the problem of [color=#0000FF]Crazyhorse2882[/color].... If a polynomial equation of degree $n>1$ and $n\in N$ has only complex root $2 + 3i$ then how many real roots does that equation?Responding to clear! Thank You!
July 5th, 2013, 09:41 PM   #35
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Re: Algebra/Polynomials

Quote:
 Originally Posted by Dacu I have proposed a solution to the problem of Crazyhorse2882....
Which one is your proposed solution?

PS : You haven't answered to my questions yet, so I repeat : May I assume all your claims are false and your version of FTA is incorrect?

July 5th, 2013, 09:45 PM   #36
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Re: Algebra/Polynomials

Quote:
 Originally Posted by Dacu If a polynomial equation of degree $n>1$ and $n\in N$ has only complex root $2 + 3i$ then how many real roots does that equation?Responding to clear!
I think you should post everything which you want to post once at a time rather than editing them in each time, it's quite hard to follow.

I have already answered that there exists no such polynomial over R[x], but if it is in C[x], there are at most n - 1 real roots but that could get smaller, so it is not exactly determinable I'd say.

July 5th, 2013, 09:55 PM   #37
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Re: Algebra/Polynomials

Quote:
Originally Posted by mathbalarka
Quote:
 Originally Posted by Dacu I have proposed a solution to the problem of Crazyhorse2882....
Which one is your proposed solution?

PS : You haven't answered to my questions yet, so I repeat : May I assume all your claims are false and your version of FTA is incorrect?
-------------------------------------------------
I repeat:
If a polynomial equation of degree $n>1$ and $n\in N$ has only complex root $2 + 3i$ then how many real roots does that equation?Responding to clear!
---------------------------------
You have complicated things with that $\Delta$......

July 5th, 2013, 10:09 PM   #38
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Math Focus: Number Theory
Re: Algebra/Polynomials

Quote:
 Originally Posted by Dacu Responding to clear!

Quote:
 Originally Posted by Dacu You have complicated things with that $\Delta$ ......
Well, you haven't been able to find another simpler method neither do you have answered to my previous questions, so that implies one thing : You claim is baseless, I was indeed right to calculate the discriminant.

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