If 5 + 6i is a root of the polynomial function f (x), which of the following must also be a root of f (x) ? - 5 - 6i 5 - 6i 6 - 5i 6 + 5i

Answer: 5-6i

The rule is that if f (x) has real number coefficients, then a root of x = a+bi pairs up with its conjugate pair of x = a - bi. In this case, a = 5 and b = 6.

5 - 6i is also the root of f (x).

Step-by-step explanation:

Given : If 5 + 6i is a root of the polynomial function f (x),

To find : which of the following must also be a root of f (x).

Solution : We have given that 5+6i is the on of the root of polynomial function f (x).

It has two parts real and imaginary part so, it is a complex number.

Real part = 5 and 6i is imaginary part.

Complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. For example, the complex conjugate of a + bi is a - bi.

a = 5, b = 6.

Then by the complex conjugate defination, Another root would be 5 - 6i

Therefore, 5 - 6i is also the root of f (x).