(*)[tex]p(x) = x^4 + ax^3 + bx^ 2 + ax + 1 = 0[/tex](adsbygoogle = window.adsbygoogle || []).push({});

where [tex]a,b \in \mathbb{C}[/tex]

I would like to prove that a complex number x makes (*) true iff

[tex]s = x + x^{-1}[/tex] is a root of the [tex]Q(s) = s^2 + as + (b-2) [/tex]

I see that that [tex]Q(x + x^{-1}) = \frac{p(x)}{x^2}[/tex]

Then to prove the above do I then show that p(x) and Q((x + ^{-1}) shares roots?

Sincerely Yours

MM23

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# Roots of a polynomial of degree 4

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