Question

Which of the following lists all the roots of x^4 =x^3 +x^2 + x+2?

F {−1, 2}
H {−2, −1}
G {−1, 2, i, −i}
J {−2, −1, i, −i}

Answer 1

G

Explanation:

`x^4-x^3-x^2-x-2=0 \\ \\ (x+1)(x^3+x-2x^2-2)=0 \\ \\ (x+1)(x(x^2+1)-2(x^2+1))=0 \\ \\ (x+1)(x-2)(x^2+1)=0 \\ \\ (x+1)(x-2)(x-i)(x+i)=0 \\ \\ x=-1, 2, i, -i`