Find all the zeros (real and complex)of the function.
-$$f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 17 x - 13$$
A)2 + 3i, 3 - 2i, 1
B)2 + 3i, 2 - 3i, -1
C)2 + 3i, 3 - 2i, -1
D)2 + 3i, 2 - 3i, 1

Question

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The zeros of the function can be found by factoring or using the Rational Root Theorem and synthetic division, followed by solving the resulting quadratic equation. For complex roots, if $a + bi$ is a root, then its complex conjugate $a - bi$ must also be a root. Given the options, the set that includes a real number and a pair of complex conjugates is the correct one. The correct answer includes $2 + 3i$ and its conjugate $2 - 3i$, along with the real number $1$, which satisfies the fundamental theorem of algebra.

Find All the Zeros (Real and Complex)of the Function f(x)=x3−5x2+17x−13f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 17 x - 13f(x)=x3−5x2+17x−13

Find All the Zeros (Real and Complex)of the Function $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 17 x - 13$