Question

If –3 i is a root of the polynomial function f(x), which of the following must also be a root of f(x)? –3 – i –3i 3 – i 3i

Answer 1

If -3 + i is a root of the polynomial function f(x), -3 - i must also be a root of f(x)

How to determine the true statement?

The root of the polynomial function is given as:

-3 + i

The above root is a complex root.

If a polynomial has a complex root, then the conjugate of the root is also a root of the function

The conjugate of -3 + i is -3 - i

Hence, if -3 + i is a root of the polynomial function f(x), -3 - i must also be a root of f(x)

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