olymmath

Putnam 1951 B6

  • Session B
  1. Assuming that all the roots of the cubic equation x3+ax2+bx+c=x^{3}+a x^{2}+b x+c= 0 are real, show that the difference between the greatest and the least roots is not less than (a2−3b)12\left(a^{2}-3 b\right)^{12} or greater than 2(a2−3b)12/3122\left(a^{2}-3 b\right)^{12 / 3^{12}}.

Dataset text PutnamGAP. Quoted with source.

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