Question

X^4 + x^3 + x^2 + x=0

Answer 1

X^4 + x^3 + x^2 + x = 0

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

x[x^2(x + 1) + 1(x + 1)] = 0

x(x + 1)(x^2 + 1) = 0 ⇔ x = 0 or x + 1 = 0 or x^2 + 1 = 0

x = 0 or x = -1 or x^2 = -1 -false

Answer: x= 0 or x = -1.