An algebra problem by Achal Jain

Algebra Level 3

Let \(f(x)= x^{5}+x+1 \), whose roots are \( \alpha_1\), \(\alpha_2\), \(\alpha_3\), \(\alpha_4\), and \(\alpha_5 \) and let \( p(x)= x^{2}-2\). If the value of \(p(\alpha_1)p(\alpha_2)p(\alpha_3)p(\alpha_4)p(\alpha_5) = \lambda\), what is \(\sqrt{|\lambda|}\)?

\(\)

Notation: \(| \cdot |\) denotes the absolute value function.

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