Find all the zeros (real and complex)of the function.
-$f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8$
A)-4, 4
B) $1 + \mathrm { i } , 1 - \mathrm { i } , - 4$
C) $1 + i , 1 - i , 4$
D) $1 - \mathrm { i } , 4 \mathrm { i }$

Question

Quizplus · Accepted Answer

To find the zeros of the function $f(x) = x^3 + 2x^2 - 6x + 8$, we can use the Rational Root Theorem, synthetic division, or factoring techniques, and then solve for $x$. Factoring by grouping or using synthetic division, we find that $x = -4$ is a root. Factoring or dividing the polynomial by $x + 4$ gives a quadratic equation, which can be solved using the quadratic formula to find the complex roots $1 + i$ and $1 - i$. Therefore, the zeros are $1 + i$, $1 - i$, and $-4$.

Find All the Zeros (Real and Complex)of the Function f(x)=x3+2x2−6x+8f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8f(x)=x3+2x2−6x+8

Find All the Zeros (Real and Complex)of the Function $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8$