Question

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

4, -8, and 2 + 5i
i know that i have to do (x+4)(x-8)(x(2+5i))(x(2-5i)) but i don't know where to go from there .

Answer 1

If \(a\) is a zero of a polynomial, then \(x-a\) is a factor. So your polynomial is
\[
(x-4)(x+8)(x-(2+5i))(x-(2-5i))
\](Notice the signs!) Now multiply out the first two brackets, multiply out the last two brackets, and then multiply the resulting brackets together.

Answer 2

ohhhh okay is x4 - 19x2 + 244x - 928 correct ? @Erin001001

Answer 3

Yes, that's perfect :)

Answer 4

thank you ! @Erin001001

Answer 5

You're welcome!