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 2016-04-02, 02:15 #1 Xyzzy     Aug 2002 22×13×163 Posts April 2016
 2016-04-02, 05:05 #2 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3×19×173 Posts A nice variation on the topic of weighing. With constraints ('lives' of robocats vaporized when p(n)>=0, i.e. between two of the roots)...
 2016-04-02, 12:52 #3 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2×11×103 Posts They forgot to mention ** is to the power of. It took me 1/2 hour of reading through past problems to figure that out. It's not clear if x is integer. Last fiddled with by a1call on 2016-04-02 at 12:54
2016-04-03, 14:40   #4
WMHalsdorf

Feb 2005
Bristol, CT

33×19 Posts

Quote:
 Originally Posted by a1call They forgot to mention ** is to the power of. It took me 1/2 hour of reading through past problems to figure that out. It's not clear if x is integer.
Let p(x)=x**3-300*x**2+a*x+b be a cubic polynomial with unknown parameters a and b that has three positive integers roots.

2016-04-03, 14:49   #5
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

226610 Posts

Quote:
 Originally Posted by WMHalsdorf Let p(x)=x**3-300*x**2+a*x+b be a cubic polynomial with unknown parameters a and b that has three positive integers roots.
Thanks for that.

Well, then the roots are too messy for me to try anything:

Last fiddled with by a1call on 2016-04-03 at 15:08

 2016-04-03, 17:50 #6 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 268516 Posts Hints: Assume that you know the three roots q, r, and s. Rewrite the equation as the product of three (x minus root). Simplify. Compare to the original equation. What have you now found about q, r, and s? Now, you will have re-discovered [URL]https://en.wikipedia.org/wiki/Vieta's_formulas[/URL]
 2016-04-07, 04:20 #7 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3×19×173 Posts If we had 14 robocats, we'd only have to "run 14 experiments" (not 16). "I see dead cats. They don't know they're dead… They're everywhere."
2016-04-12, 01:02   #8
jwaltos

Apr 2012
Oh oh.

1CF16 Posts

Quote:
 Originally Posted by Batalov If we had 14 robocats, we'd only have to "run 14 experiments" (not 16). "I see dead cats. They don't know they're dead… They're everywhere."
A subcategory exists of unborn cats that do not yet realize they will be alive..epistemic observation.

Last fiddled with by jwaltos on 2016-04-12 at 01:04 Reason: not required

 2016-05-02, 02:45 #9 Xyzzy     Aug 2002 204348 Posts
2016-05-05, 05:27   #10
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

9,973 Posts

Quote:
 Originally Posted by Xyzzy https://www.research.ibm.com/haifa/p...April2016.html
Quote:
 If x**3+300*x**2+a*x+b = (x-x1)(x-x2)(x-x3), then x1+x2+X3=300
I have a problem with that: according with the math I learned in elementary school (grade 8), if x1+x2+X3=300, then the polynomial would be x**3 - 300*x**2.... and not plus...

Last fiddled with by LaurV on 2016-05-05 at 05:41

2016-05-05, 05:42   #11
axn

Jun 2003

19·283 Posts

Quote:
 Originally Posted by LaurV I have a big problem with that: according with the math I learned in elementary school (grade 8), if x1+x2+X3=300, then the polynomial would be x**3 - 300*x**2.... and not plus...
Yes. And the problem (https://www.research.ibm.com/haifa/p...April2016.html) calls for p(x)=x**3-300*x**2+a*x+b. The +300 is just a typo in the solution.

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