Product of Values on Roots

Algebra Level 5

Denote by x1, x2, x3, x4x_1,\ x_2,\ x_3,\ x_4 the roots of the polynomial f(x)=x44x312x2+1f(x)=x^4-4x^3-12x^2+1. Denote g(x)=x2+2g(x)=x^2+2. Find the value of the product g(x1)g(x2)g(x3)g(x4). g(x_1)g(x_2)g(x_3)g(x_4) .

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