Find the requested polynomial.
-Find a polynomial function of degree 3 with 2, i, -i as zeros.
A) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + x - 2$
B) $f ( x ) = x ^ { 3 } - 2 i x ^ { 2 } + x - 2 i$
C) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + i x - 2 i$
D) $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - x + 2$

Question

Find the requested polynomial.
-Find a polynomial function of degree 3 with 2, i, -i as zeros. 
A) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + x - 2$
B) $f ( x ) = x ^ { 3 } - 2 i x ^ { 2 } + x - 2 i$
C) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + i x - 2 i$
D) $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - x + 2$

Quizplus · Accepted Answer

Given the zeros 2, i, and -i, the polynomial can be constructed by multiplying the factors (x - 2), (x - i), and (x + i). Multiplying these factors together yields $x^3 - 2x^2 + x - 2$, which matches option A.

Find the Requested Polynomial f(x)=x3−2x2+x−2f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + x - 2f(x)=x3−2x2+x−2

Find the Requested Polynomial $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + x - 2$