Demonstrate if (1-x1)(1-x2)(1-x3)(1-x4)=5 if x1,x2,x3,x4 are roots of the equation x^4 + x^3 + x^2 + x +1 =0

If x^4+x^3+x^2+x+1 = 0.To show that
(1-x1)(1-x2)(1-x3)1-x4) = 5,

Where x1,x2,x3 and x4 are the
roots of the
equation.

Proof.

If  f(x) =
ax^n+a1x^n-1 +a3x^-3 +....+an-*x+an = 0 has the roots  x1,x2,x3,..and xn,
then

f(x) = x^n +a1x^-1+a2x^(n-2)+....an-1*x+an =
(x-x1)(x-x2)(x-x3)...(x-xn) is identity.

So in this
case case, x^4+x^3+x^2+x+1 =
(x-x1)(x-x2)(x-x3)(x-x4)...........(1).

Since above
equation is an identity, we put x= 1 on both
sides:

1^4+1^3+1^2+1^1+1 =
(1-x1)(1-x2)(1-x3)(1-x4)

5 = (1-x1)(1-x2)(1-x3)(1-x4) which
estabilses the proof for the enunciation.