Question

Write a polynomial function with a minimum degree with real coefficients whose zeros are listed. Write the polynomial in standard form.

1) 4i and sqrt of 5

2) 3,-1 and -1+2i

Answer 1

When you have zeros \(r_1,r_2\), then you will have a polynomial: \[
(x-r_1)(x-r_2)
\]

Answer 2

One thing to be careful of though, is that for any real coefficient polynomial, when you have a complex root \(a+bi\), then \(a-bi\) must also be a root to ensure the coefficients are real.