Question

If a polynomial function f(x) has roots 4 – 13i and 5, what must be a factor of f(x)?

Answer 1

The factor of f(x) is (x-(4-13i))

If a polynomial function f(x) has roots 4 – 13i and 5

One of the complex roots is 4-13i

If we have one complex root then there should be one more complex root.

What is the complex root?

complex roots come in pairs like (a+ib) and  (a-ib)

so another complex root for 4-13i  is 4+13i

If 'a' is a root then the factor is (x-a)

4+13i is a root

So the factor is (x-(4-13i))

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