20190925, 17:15  #1 
Jul 2014
3×149 Posts 
roots of cubics
Hi,
say a cubic equation intersects the yaxis at a point where it's derivative is 0 and also intersects the yaxis at one other point (so it touches the yaxis twice), wouldn't it have to have one root that isn't real? Will 
20190925, 17:26  #2  
Nov 2003
2^{2}·5·373 Posts 
Quote:
IMPOSSIBLE. It is an elementary exercise to see why. There are two different reasons. 

20190925, 17:28  #3 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2·41·71 Posts 
It is possible to have repeated roots of cubic equations.

20190925, 17:38  #4 
(loop (#_fork))
Feb 2006
Cambridge, England
13×491 Posts 
No: if any polynomial has f(t)=0 and f'(t)=0 for the same t, that t is a multiple root of the polynomial (that is, the polynomial is divisible by (xt)^2 )

20190925, 18:25  #5  
Nov 2003
7460_{10} Posts 
Quote:
Sigh..... Bob runs screaming from the classroom...…...Has everyone forgotten basic algebra???? Reread what the OP wrote!! He said that the curve itself hits the yaxis twice......Once where its derivative is 0. i.e. he wants f(0) to have TWO DIFFERENT VALUES. This is not a function!!! [y = cubic polynomial in x] And, of course, a cubic can NEVER have a single imaginary root......Imaginary roots come in pairs! 

20190925, 18:54  #6 
"Curtis"
Feb 2005
Riverside, CA
2·2,339 Posts 
Bob
It's pretty clear the OP meant xaxis, rather than yaxis. Your answer about imaginary (complex) roots always coming in pairs helps whether he typo'ed yaxis or not, though. 
20190925, 19:16  #7 
Nov 2003
16444_{8} Posts 
I assume that people mean what they write. I assume that they proofread before posting.

20190925, 19:18  #8 
Nov 2003
2^{2}·5·373 Posts 

20190925, 19:20  #9 
(loop (#_fork))
Feb 2006
Cambridge, England
13×491 Posts 

20190925, 19:24  #10  
Nov 2003
7460_{10} Posts 
Quote:
write, especially when discussing a subject (such as mathematics) where it is possible to always use precise language. 

20190925, 20:01  #11 
"Curtis"
Feb 2005
Riverside, CA
2×2,339 Posts 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Extracting kth roots mod m  Dubslow  Miscellaneous Math  8  20121213 21:35 
Roots of 1 mod 2^n  fenderbender  Miscellaneous Math  17  20101116 16:25 
primtive roots mod p^2  Peter Hackman  Math  2  20071024 06:41 
Primitive Roots  Numbers  Math  16  20050921 23:41 
What is the roots of NFS algorithm?  Annunaki  NFSNET Discussion  7  20030729 16:01 