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

Question

Quizplus · Accepted Answer

A polynomial with given zeros $(a,b,c)$ has the form $(x-a)(x-b)(x-c)$. Therefore, the polynomial with zeros $(0,4-i,4+i)$ is $(x-0)(x-(4-i))(x-(4+i))$. After simplification, we get the polynomial $x^3-8x^2+17x$, which is option 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 $0,4 - i , 4 + i$