Write a polynomial f (x) that meets the given conditions.
-Degree 3 polynomial with integer coefficients with zeros $- 7 i$ and $\frac { 4 } { 5 }$
A) $f ( x ) = 25 x ^ { 3 } - 75 x ^ { 2 } + 296 x - 112$
B) $f ( x ) = 25 x ^ { 3 } - 5 x ^ { 2 } - 264 x + 112$
C) $f ( x ) = 5 x ^ { 3 } - 4 x ^ { 2 } - 245 x + 196$
D) $f ( x ) = 5 x ^ { 3 } - 4 x ^ { 2 } + 245 x - 196$

Question

Quizplus · Accepted Answer

The polynomial must have integer coefficients, so the complex conjugate $7i$ must also be a zero. The polynomial is formed by $(x + 7i)(x - 7i)(x - \frac{4}{5})$, which simplifies to $ (x^2 + 49)(5x - 4) $, resulting in the polynomial $5x^3 - 4x^2 + 245x - 196$.

Write a Polynomial F (X) That Meets the Given Conditions −7i- 7 i−7i

Write a Polynomial F (X) That Meets the Given Conditions $- 7 i$