33i got something at (in eng this time)
http://books.google.co.in/books?id=0ZwmLz_UTYoC&pg=PA60&dq="degree+of+tangency"#PPA60,M1
also
...
http://books.google.co.in/books?ct=result&q="degree+of+tangency"&btnG=Search+Books
Why it is said that no of roots of x3=0 is 3 repeated roots...
Then why sin(x)=1 has only one root in (0,pi)
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12 Answers
62hmm.. interesting...
i get ur question.. it is very thought provoking... i will post somting may be in a bit.. cos i need to be convinced about my arguments first :)
62see my first "guess"
is that the concept of repeated roots is only for polynomials...
sin is not a polynomial in that sense... of course taylor's expansion does make everythign close to a polynomial...
33Don't know sir said its related to degree of tangency or something like that......
x3 has degree of tangency 3 at x=0....
as up to second derivative it is zero at x=0;
this is true for sinx also at pi/2 cosx=0...
so should be two solns...
but he said its about convention so sinx =1 has one soln....
i think....
62hmm.. i guess ur sir has some point..
but i wud be interested in knowing the degree of tangency.. cos i never heard of something like this!
33
1i think no. of roots are defined by power of the polynomial.............as xn has n roots similarly x3 has 3 roots
bt if we take sin(x)=1
=> sin-1(1)=x ,so here also it depends upon power of x and second thing is interval in which it lies.............
i don't know hw right i m..........
341The fundamental theorem of algebra is related to polynomials.
It says that the polynomial of degree n
aoz^n+a1z^{n-1}+...+an = 0
has at least one root in the field of complex numbers
From factor theorem we deduce that it has exactly n roots counting repeated roots.
sine is not regarded as a polynomial and hence the theorem doesnt apply
39i was not fully satisfied with the discussion, so posted in mathlinks again...
u can see the explanation here
http://www.mathlinks.ro/viewtopic.php?t=304586
3well i have read something abt repeated roots.
if f(∂)=0 and f'(∂)=0 then ∂ is said to be a repeated root of f(x)