Answer:
5 - 6i must also be a root of f(x)
Step-by-step explanation:
Complex conjugates states that the two complex numbers are conjugates of each other if they have the same real part and their imaginary parts are negatives of each other i.e, the complex conjugate of a + bi is a - bi where i is imaginary.
Conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a-bi is also a root of that polynomial.
Given: if 5+ 6i is a root of the polynomial function f(x).
then,
by the conjugate root theorem;
5 - 6i is also be a root of the polynomial f(x).
