Write a polynomial in standard form that has the following characteristics.

Question

leading coefficient: 4

zeros: 0, -8, 5i, 2

Answer 1

If you want only real coefficients, then the complex conjugate of any complex zero is also a zero. You will have minimum degree of 5, and the zeros are

0

-8

5i

-5i

2

Then

p(x) = 4x(x + 8)(x - 5i)(x + 5i)(x - 2)

You can expand this to standard form if you wish.