Find a polynomial with the given zeros. $$0,4 - i , 4 + i$$
A) $\quad x ^ { 3 } + 17 x ^ { 2 } - 4 x$
B) $x ^ { 3 } - 4 x ^ { 2 } + 16 x$
C) none of these
D) $\quad x ^ { 3 } - 8 x ^ { 2 } + 17 x$
E) $\quad x ^ { 3 } - 8 x ^ { 2 } + 17$

Question

Quizplus · Accepted Answer

Since each zero is of the form $a+bi$, we know that its conjugate $a-bi$ must also be a zero. Therefore, the polynomial with these three zeros is $$(x-0)(x-(4-i))(x-(4+i))(x-(4-i))(x-(4+i)) = (x^2-8x+17)(x-0) = \boxed{x^3-8x^2+17x}$$ which is answer choice $\textbf{(D)}$.

Find a Polynomial with the Given Zeros 0,4−i,4+i0,4 - i , 4 + i0,4−i,4+i

Find a Polynomial with the Given Zeros $0,4 - i , 4 + i$