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 { x }^{ 2 } +2qx+r=0 q x 2 { x }^{ 2 } +2rx+p=0 r x 2 { x }^{ 2 } +2px+q=0

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

α \alpha is irrational and positive α \alpha is real and positive α \alpha is imaginary α \alpha is real and negative

Rounak Chatterjee by rounak chatterjee , 21, India

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