Give an expression for f (x) with leading coefficient -4, of degree 3, and having roots x=5, x=1+4i, and x=1-4i.

Question

Give an expression for f (x) with leading coefficient -4, of degree 3, and having roots x=5, x=1+4i, and x=1-4i.

final answer should not contain any i's.

f(x)=_________ is a polynomial of degree 3 with the given roots and leading coefficient.

Answer 1

f(x) = - 4(x - 5)(x - 1 - 4i)(x - 1 + 4i) = - 4(x - 5)(x² - 2x + 17)