# An algebra problem by rounak chatterjee

Algebra Level 3

Let p,q,r be positive real numbers,not all equal,such that any two of the following:--- p$${ x }^{ 2 }$$+2qx+r=0 q$${ x }^{ 2 }$$+2rx+p=0 r$${ x }^{ 2 }$$+2px+q=0

has a common root $$\alpha$$. Which of the following is true about alpha?

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