Question

Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and zeros of 2 and 4+i.

Answer 1

A few things --

1) Complex roots always come in "conjugate" pairs. In other words, if you have " a + bi" as one root, then "a - bi" must also be a root.

2) If a polynomial has a root at "k", then (x-k) is a factor.

You should now be able to write something that looks like ( x - root 1) * (x - root 2) * ( x- root 3)

From there, factor that out carefully and that should be your polynomial. :)