Let \(a,b,c \) be positive real numbers. Determine the largest total number of real roots that the following three polynomials may have among them: \(ax^2 + bx + c,\)\(bx^2 + cx + a, \)\(cx^2 + ax + b. \)

They are all quadratics, that can have two real roots, so the largest total number of real roots is 6.

AoPS. Morrivillle,

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