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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:   \(ax^2 + bx + c,\)\(bx^2 + cx + a, \)\(cx^2 + ax + b. \)

 Nov 16, 2019
 #1
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They are all quadratics, that can have two real roots, so the largest total number of real roots is 6.

 Nov 16, 2019
 #2
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AoPS. Morrivillle,

 

Try not to post homework questions.

 Nov 16, 2019
 #3
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AoPS.Morrisville PLEASE do not post homework questions on this forum

 Nov 16, 2019

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