MATH QUESTION!! (help)?

Question

Find the complex zeros of this polynomial function. (Select all that apply.)
f(x) = x^4 + 5x^2 + 4

how do you do this? thanks so much!

Answer 1

x^4 + 5x^2 + 4 is a quadratic in x^2, so
x^4 + 5x^2 + 4 =
x^4 + 5x^2 + (5/2)^2 - 25/4 + 4 =
(x^2 + 5/2)^2 - 25/4 + 16/4 =
(x^2 + 5/2)^2 - 9/4 =
(x^2 + 5/2 - 3/2)(x^2 + 5/2 + 3/2) =
(x^2 + 1)(x^2 + 4) =
(x + i1)(x - i1)(x + i2)(x - i2) = 0 for roots:
x = ± i, ± i2