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: ax2+bx+c,bx2+cx+a,cx2+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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+143 
