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

Quizplus · Accepted Answer

Complex zeros of polynomials with real coefficients come in conjugate pairs, so if 5i is a zero, -5i is also a zero. The Rational Root Theorem helps identify possible rational zeros based on the coefficients, leading to $-\frac{8}{7}$ as the correct rational zero, not its reciprocal or positive version.

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