$$\text { Write a third-degree polynomial equation with real coefficients and the roots } 4 , - i \text {. }$$
A)$\quad x ^ { 3 } - 4 = 0$
B) $\quad x ^ { 3 } - 4 x ^ { 2 } + x - 4 = 0$
C) $\quad x ^ { 3 } - 16 = 0$
D) $\quad x ^ { 3 } - 5 x ^ { 2 } - x + 16 = 0$
E) none of these

Question

$$\text { Write a third-degree polynomial equation with real coefficients and the roots } 4 , - i \text {. }$$ 
A)$\quad x ^ { 3 } - 4 = 0$
B) $\quad x ^ { 3 } - 4 x ^ { 2 } + x - 4 = 0$
C) $\quad x ^ { 3 } - 16 = 0$
D) $\quad x ^ { 3 } - 5 x ^ { 2 } - x + 16 = 0$
E) none of these

Quizplus · Accepted Answer

The product of the roots is 4*(-i) = -4i, and the sum of the roots is 4 + (-i) = 4 - i. Therefore, the polynomial equation is x^3 - (4 - i)x^2 + (-4i)x + 16 = 0.

Write a third-degree polynomial equation with real coefficients and the roots 4,−i. \text { Write a third-degree polynomial equation with real coefficients and the roots } 4 , - i \text {. } Write a third-degree polynomial equation with real coefficients and the roots 4,−i.

$\text { Write a third-degree polynomial equation with real coefficients and the roots } 4 , - i \text {. }$