A Root-Five Quartic

★ 6/10Quadratic Equations algebra Polynomials Discriminant

Problem

Find the sum of the integer parts of all positive real numbers $x$ satisfying

x^4 - x^3 - 2\sqrt{5}x^2 - 7x^2 + \sqrt{5}x + 3x + 7\sqrt{5} + 17 = 0.

Answer

Solution

Difficulty	6/10
Topics	Quadratic Equations, algebra, Polynomials, Discriminant

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