x^4+2x^3+2x-1
hint: -i is a zero
I'm not sure how to approach this question. I tried using the synthetic division but that just seems to complicate it. Maybe I'm doing it wrong. Pls help :D
Did you know that all complex roots come in conjugate pairs?
So if -i is a zero, then so is +i
and x^2+1 must be a factor of your expression
(if x^2 + 1 = 0 , then x = ± i )
by long algebraic division,
x^4 + 2x^3 + 2x - 1 = (x^2+1)(x^2 + 2x - 1)
so solve x^2 + 2x-1 = 0
in this case I would use completing the square.
x^2 + 2x = 1
x^2 + 2x + 1 = 1+1
(x+1)^2 = 2
x+1 = ±√2
x = -1 ± √2
4 zeros: ±i , -1 ± √2