Number Theory: The discriminant is used to determine whether multiple roots for a polynomial exist. We consider the special case of cubics in the form f(x) = 4x^3 -ax - b. We show that the discriminant 16[(x1-x2)(x2-x3)(x3-x1)]^2 equals a^3 - 27b^2 using symmetric polynomials.
Tagged under: Mathematics,number,theory,cubic,polynomial,discriminant,roots,zeros,elliptic,curve,modular,function,symmetric
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