Re: [Math4u] quadratic equation

A function does not have ROOTS, it may have ZEROS.  An equation has ROOTS and the graph of the associated function may have ZEROS.

 

Buck Dick

sanjiva dayal <sanjivadayal@yahoo.com> wrote:

Dear Buck,
Function and equation are different entities. f(x) is
a function and f(x)=0 is an equation. According to
fundamental theorem of algebra, a polynomial function
of degree n has exactly n roots in the set of complex
numbers and equal roots are counted as different. But
solution of a polynomial equation f(x)=0 are those
different numbers which satisfy this equation and
there are no equal solutions. So the polynimial
function f(x)=x^3 has three roots 0,0,0 but the
polynomial equation x^3=0 has only one solution, which
is 0.
So the polynomial function x^5-4x^3 has 5 roots
0,0,0,-2,2 but equation x^5-4x^3=0 has only 3
solutions 0,-2,2.
Sanjiva

--- Buck Dick <kcubar34@yahoo.com> wrote:

> No one ever credited mathematicians with politeness.
> BUT, thus far I haven't seen anyone give an answer
> that is consistent with the Fundamental Theorem of
> Algebra. Over the domain of complex numbers a fifth
> degree polynomial equation must have exactly five
> roots, not three, not two, but five, and of course,
> the multiplicity of the root gives valuable
> information about the graph of the related function
> in a Cartesian Coordinate System.
>
> Buck Dick
>
> Vinaire <vinaire@yahoo.com> wrote:
> Blunt honesty can be impolite.
>
> Vinaire
>
>
> ----- Original Message ----
> From: sanjiva dayal <sanjivadayal@yahoo.com>
> To: Math4u@yahoogroups.com
> Sent: Monday, September 17, 2007 6:59:22 AM
> Subject: Re: [Math4u] quadratic equation
>
> Hi,
> You are wrong. x=0 is also an answer.
> Sanjiva
>
> --- "rolandjo@juno. com" <rolandjo@juno. com> wrote:
>
> > x^5 = 4x^3
> > <?xml:namespace prefix = o ns =
> > "urn:schemas- microsoft- com:office: office" />
> > x^5 – 4x^3 = 0
> >
> > Divide both sides of the equation by x^3
> >
> > x^2 - 4 = 0
> >
> > ( x + 2 ) ( x – 2 ) = 0
> >
> >
> > X + 2 = 0 or X - 2 = 0; therefore, x = -2 or 2.
> >
> >
> > Roland Josefek
> >
> >
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>
> Sanjiva Dayal, B.Tech.(I.I. T. Kanpur)
> Address:A-602, Twin Towers, Lakhanpur,
> Kanpur-208024, INDIA.
> Phones:+91-512- 2581532,2581426.
> Mobile:9415134052
> Business email:sanjivadayal@ yahoo.com
> Personal email:sanjivadayal@ hotmail.com
>
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Sanjiva Dayal, B.Tech.(I.I.T. Kanpur)
Address:A-602, Twin Towers, Lakhanpur, Kanpur-208024, INDIA.
Phones:+91-512-2581532,2581426.
Mobile:9415134052
Business email:sanjivadayal@yahoo.com
Personal email:sanjivadayal@hotmail.com

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