The question is :"The polynomial 3x(adsbygoogle = window.adsbygoogle || []).push({}); ^{5}-250x^{3}+735x is interesting because it has the maximum possible number of relative extrema and points of inflection at integer lattice points for a quintic polynomial. What is the sum of the x-coordinates of these points?"

I think the answer is 0, but it's wrong.

My solution is :"The first derivative is 15x^{4}-750x^{2}+735, whose roots are -7,-1,1 and 7. The second derivative is 60x^{3}-1500x,whose roots are 0,-5,5. Then, the sum is 0."

The HMMT solution is "The first derivative is 15x^{4}-750x^{2}+735, whose roots sum to 750/15=50. The second derivative is 60x^{3}-1500x,whose roots sum to 1500/60=25, for a grand total of 75."

I really can't understand how it get the sum 50 and 25...Please help me.

Thanks...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calculus problems (hmmt)

**Physics Forums | Science Articles, Homework Help, Discussion**