Question

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 1

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.

Answer 2

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

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).