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probability that all roots

Source: Brazil Undergrad MO - Galois-Noether 2018 #15

November 26, 2019
probabilityBrazilian Math Olympiadcollege contestsalgebra

Problem Statement

A real number to to is randomly and uniformly chosen from the [āˆ’3,4] [- 3,4] interval. What is the probability that all roots of the polynomial x3+ax2+ax+1 x ^ 3 + ax ^ 2 + ax + 1 are real?
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