- #1
fayeshin
- 5
- 0
The question is :"The polynomial 3x5-250x3+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 15x4-750x2+735, whose roots are -7,-1,1 and 7. The second derivative is 60x3-1500x,whose roots are 0,-5,5. Then, the sum is 0."
The HMMT solution is "The first derivative is 15x4-750x2+735, whose roots sum to 750/15=50. The second derivative is 60x3-1500x,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...
I think the answer is 0, but it's wrong.
My solution is :"The first derivative is 15x4-750x2+735, whose roots are -7,-1,1 and 7. The second derivative is 60x3-1500x,whose roots are 0,-5,5. Then, the sum is 0."
The HMMT solution is "The first derivative is 15x4-750x2+735, whose roots sum to 750/15=50. The second derivative is 60x3-1500x,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...