Suppose x=2-7i is a zero of a polynomial function. What would need to be two linear factors of the polynomial equation?

Question

Suppose x=2-7i is a zero of a polynomial function. What would need to be two linear factors of the polynomial equation?

Answer 1

Complex roots always come in conjugate pairs, so if 2-7i is root so is 2+7i.  The two linear factors then would be:

 

(x - (2-7i))*(x - (2+7i))