Cubic polynomial and others

Algebra Level pending

f ( x ) f(x) is a cubic polynomial with constant coefficients. If the difference between it's maximum and minimum can't be less than ( 1 α ) t h (\frac {1}{\sqrt α})^{'th} of the ratio of the coefficient of x x and the coefficient of x 3 x^3 , find α α .


The answer is 3.000.

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