Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - 18 x + 20$$
A) $1 + i , 1 - i , - 10$
B) $1 + i , - 10,10$
C) $1 + i , 1 - i , 10$
D) $1 + \mathrm { i } , 1 - \mathrm { i } , 10 \mathrm { i }$

Question

Quizplus · Accepted Answer

The polynomial can be factored or solved using techniques such as synthetic division or the Rational Root Theorem. The correct zeros are $1 + i$, $1 - i$, and $-10$, which correspond to the complex conjugate pair (since complex roots of polynomials with real coefficients come in conjugate pairs) and a real root.

Find All Complex Zeros of the Polynomial Function f(x)=x3+8x2−18x+20f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - 18 x + 20f(x)=x3+8x2−18x+20

Find All Complex Zeros of the Polynomial Function $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - 18 x + 20$