Use the given zero to find all the zeros of the function. ? Function Zero 7x³ + 8x² + 175x + 200 5i ? ? A)±5i, $\frac { 8 } { 7 }$ B)±5i, $- \frac { 8 } { 7 }$ C)±5i,-8 D)±5i, $- \frac { 7 } { 8 }$ E)±5i, $\pm \frac { 8 } { 7 } i$

Question

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Given a complex zero 5i for a polynomial with real coefficients, its conjugate -5i is also a zero. The polynomial is of degree 13, indicating there are 13 roots in total. Since 5i and -5i are two of them, we need to find the remaining roots. The options suggest looking for real roots or additional complex roots. The correct answer must include the conjugate pair ±5i and any real roots. The option that includes ±5i and a real root that is not a conjugate (since the given root is purely imaginary) is the correct one. The option B) ±5i, $- \frac { 8 } { 7 }$ correctly identifies the conjugate pair and a real root, fitting the criteria for a polynomial with real coefficients.

Use the Given Zero to Find All the Zeros of the Function