Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = 3 x ^ { 4 } - 10 x ^ { 3 } + 20 x ^ { 2 } - 40 x + 32$$
A) $- \frac { 4 } { 3 } , - 2 , - 2 i , 2 i$
B) $\frac { 4 } { 3 } , 2 , - \mathrm { i } , \mathrm { i }$
C) $\frac { 2 } { 3 } , 2 , - 4 \mathrm { i } , 4 \mathrm { i }$
D) $\frac { 4 } { 3 } , 2 , - 2 \mathrm { i } , 2 \mathrm { i }$

Question

Quizplus · Accepted Answer

The polynomial can be factored or solved using techniques such as synthetic division or the Rational Root Theorem, leading to the zeros $\frac{4}{3}$, $2$, $-2i$, and $2i$. These zeros satisfy the polynomial equation, including the complex conjugate pair $-2i$ and $2i$, which are common in polynomials with real coefficients.

Find All Complex Zeros of the Polynomial Function f(x)=3x4−10x3+20x2−40x+32f ( x ) = 3 x ^ { 4 } - 10 x ^ { 3 } + 20 x ^ { 2 } - 40 x + 32f(x)=3x4−10x3+20x2−40x+32

Find All Complex Zeros of the Polynomial Function $f ( x ) = 3 x ^ { 4 } - 10 x ^ { 3 } + 20 x ^ { 2 } - 40 x + 32$