For the polynomial, one zero is given. Find all others.
-$$P ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 13 x - 20 ; 4$$
A) $1 + 2 i , 1 - 2 i$
B) $- 1 + 2 i , - 1 - 2 i$
C) $1 + \sqrt { 5 } , 1 - \sqrt { 5 }$
D) $1 + \sqrt { 5 } i , 1 - \sqrt { 5 } i$

Question

Quizplus · Accepted Answer

Given one zero is 4, we can use synthetic division or polynomial division to find the quotient when $P(x)$ is divided by $x - 4$. The quotient will be a quadratic polynomial, whose roots can be found using the quadratic formula or factoring. The division gives us $x^2 - 2x + 5$, whose roots are $1 + 2i$ and $1 - 2i$, confirming option A as correct.

For the Polynomial, One Zero Is Given P(x)=x3−6x2+13x−20;4P ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 13 x - 20 ; 4P(x)=x3−6x2+13x−20;4

For the Polynomial, One Zero Is Given $P ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 13 x - 20 ; 4$