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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