Answer
$f(x)=x^4+3x^3-11x^2+9x+70$
Work Step by Step
A polynomial function with the given zeros could be:
$$f(x)=(x-(-5))(x-(-2))(x-(2+\sqrt3i))(x-(2-\sqrt3i))$$
$$f(x)=(x+5)(x+2)(x^2-(2+\sqrt3i)x-(2-\sqrt3i)x-(2+\sqrt3i)(2-\sqrt3i))$$
$$f(x)=(x^2+7x+10)(x^2-2x-\sqrt3 ix-2x+\sqrt3ix-(4-3(-1)))$$
$$f(x)=(x^2+7x+10)(x^2-4x+7)$$
$$f(x)=x^4-4x^3+7x^2+7x^3-28x^2+49x+10x^2-40x+70$$
$$f(x)=x^4+3x^3-11x^2+9x+70$$
