Quadratika -2 - Inspired by Sandeep Bhardwaj!

Algebra Level 5

\[ \large \begin{cases} {x^2_1 + px_1 +q = x_2} \\ {x^2_2 + px_2 +q = x_3} \\ {x^2_3 + px_3 +q = x_1} \\ \end{cases} \]

Let \(p,q\) be real numbers with \(\alpha < \beta\) be the roots of the equation \(x^2 +(p-1)x+q=0\).

What is the maximum number of solutions of the system of equations above where \(x_1,x_2,x_3 \in [\alpha,\beta] \) is?

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