The Sixth of Seven Problems - HMM... Yeah .... EASIEST PROBLEM ON THE INTERNET
Given a set of polynomials ranging from 1st to nth degree where each coefficient (except for leading,it is one) is a random number chosen between 0 and n-1(not necessarily distinct numbers),find , if the probability that all polynomials in the set has a sum of roots as 0 for n =x is .
The answer is 5.
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1 solution
Since all the trait of having a sum of roots of 0 means that having the second coefficient as 0(by Vieta) all the "probability" defined above is is the product of the chances for each individual polynomial that the second variable is 0.That is 1/of the degree of the polynomial.Therefore f(x) is the factorial and 5!/24 =5.