# 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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