Product of Values on Roots

Algebra Level 5

Denote by \(x_1,\ x_2,\ x_3,\ x_4\) the roots of the polynomial \(f(x)=x^4-4x^3-12x^2+1\). Denote \(g(x)=x^2+2\). Find the value of the product \[ g(x_1)g(x_2)g(x_3)g(x_4) . \]

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