April 2016

[Xyzzy]

https://www.research.ibm.com/haifa/p...April2016.html

[Batalov]

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)...

[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.

[WMHalsdorf]

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.

[a1call]

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:

Link

[Batalov]

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]

[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."

[jwaltos]

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.

[Xyzzy]

https://www.research.ibm.com/haifa/p...April2016.html

[LaurV]

Originally Posted by Xyzzy

https://www.research.ibm.com/haifa/p...April2016.html

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...

[axn]

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.