Zeros of polynomials with real coefficients always come in conjugate pairs. Thus, another zero is 1-I. These two zeros mean that
(x-1+I)(x-1-I) = x^2 -2x -2
is a factor of F(x).
By polynomial division, we find the remaining factor to be x+10.
The zeros of F(x) are
1 ± I, -10.
(x-1+I)(x-1-I) = x^2 -2x -2
is a factor of F(x).
By polynomial division, we find the remaining factor to be x+10.
The zeros of F(x) are
1 ± I, -10.