Inspired by an IMO problem!

Algebra Level 5

Let \(a\) and \(b\) be two real numbers. If \( x^4+ax^3+bx^2+ax+1=0 \) has two distinct real solutions \(\alpha\) and \(\beta\) such that \(\alpha*\beta\not=1\). Which of the following answer choices must be true for the given equation?

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