A polynomial has one root that equals 5 - 7i. Name one other root of this polynomial.Answer hereSUBMITarrow_backPREVIOUS

In the context of polynomials with real coefficients, complex roots occur in conjugate pairs. Therefore, if one root of the polynomial is $5 - 7i$, then the other root must be its complex conjugate, which is found by changing the sign of the imaginary part.

Final Answer

The other root of the polynomial is $5 + 7i$.

This follows from the property that if $a + bi$ is a root (where $a$ and $b$ are real numbers and $i$ is the imaginary unit), then $a - bi$ must also be a root of the polynomial. In this case, with $a = 5$ and $b = 7$, the conjugate is straightforwardly determined as $5 + 7i$.