Question

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

3, -13, and 5 + 4i

f(x) = x4 - 8x3 - 12x2 + 400x - 1599

f(x) = x4 - 200x2 + 800x - 1599

f(x) = x4 - 98x2 + 800x - 1599

f(x) = x4 - 8x3 + 12x2 - 400x + 1599

Answer 1

if \(\alpha\) is a zero of the polynomial \(p(x)\) then \(x-\alpha\) is a factor of \(f(x)\).

Answer 2

if \(z=a+ib\) is a zero of the polynomial \(p(x)\) then \(\overline{z}=a-ib\) is also a zero of \(f(x)\).

Answer 3

I dont understand @helder_edwin which option would that apply to

Answer 4

well u have two options:
(i) replace the zeros u r given in each choice and see which one turns zero on all three (really long), or
(ii) multiply the factors u obtain from my two previous posts.

Answer 5

como on. do it.
\[ \large p(x)=(x-3)(x+13)[x-(5+4i)][x-(5-4i)] \]