For the polynomial, one zero is given. Find all others.
$P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 12 x + 14 ; 1 + i$
A) -7,7
B) 1-i, 7i
C) 1-i, 7
D) 1-i,-7

Question

For the polynomial, one zero is given. Find all others.
$P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 12 x + 14 ; 1 + i$
A)  -7,7 
B)  1-i, 7i 
C)  1-i, 7 
D)  1-i,-7

Quizplus · Accepted Answer

Since the coefficients of the polynomial are real, the complex roots must occur in conjugate pairs. Given one root is $1+i$, its conjugate $1-i$ is also a root. Using synthetic division or factoring, the remaining root is found to be $-7$.

For the Polynomial, One Zero Is Given P(x)=x3+5x2−12x+14;1+iP ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 12 x + 14 ; 1 + iP(x)=x3+5x2−12x+14;1+i

For the Polynomial, One Zero Is Given $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 12 x + 14 ; 1 + i$