Answer:
The other root of the polynomial is 5+7i.
Step-by-step explanation:
According to the complex conjugate root theorem, if a complex number is a root of a polynomial, then its conjugate is also a root of that polynomial.
It means, if a+ib is a complex root of a polynomial, then its conjugate a-ib is also the root of that polynomial.
It is given that the a polynomial has one root that equals 5-7i.
To find the conjugate of a complex number the sign of imaginary part is changed.
The conjugate of 5-7i is 5+7i.
A polynomial has one root that equals 5-7i, using complex conjugate root theorem 5+7i is the other root of this polynomial.
