We have to solve for x: x^3 +x^2 +x +1 = 0

x^3 +x^2 +x +1 = 0

=> x^2( x + 1) + 1(x + 1) = 0

=> (x^2 + 1)(x + 1) = 0

x + 1 = 0

=> x = -1

x^2 + 1 = 0

=> x^2 = -1

=> x = i , -i

The values of x are -1 , i , -i

Given the equation:

x^3+ x^2 + x +1 = 0

We need to find x values that satisfies the equation.

First we will simplify by factoring.

We will factor x^2 from the first two terms.

==> x^2 ( x+1) + x+1 = 0

Now we will factor x+1

==> (x+1)*(x^2+1) = 0

==> x+1 = 0 ==> x1= -1

==> x^2 + 1 = 0 ==> x= +-i

Then, there are 3 roots for the equation.

==> x= { -1, i, -i}