Question

Let p (x)= x⁵ + x² + 1 have roots x₁, x₂, x₃, x₄ and x₅, g (x) = x² - 2 , then find the value of g (x₁)g (x₂)g (x₃)g (x₄)g (x₅) - 30g (x₁x₂ x₃x₄ x₅).

Answer 1

Given

p(x) = x⁵ + x² + 1 = 0 has roots x₁,x₂, .....x₅  then that equation q (x) whose roots are square of the roots of p (x) is

Alternative solution:

Let us form that equation having roots y  = g(x_i). Then