Question

find (complex) zeros

f(x)=x^4+5x^2+4

Answer 1

f(x)=x^4+5x^2+4
= (x^2 + 4) (x^2 + 1)
x = +/-2i, +/-i

Answer 2

it's easier than you think.

Answer 3

\[f(x)=x^4+5x^2+4\]\[Let~~x^2=a\]\[f(x)=a^2+5a+4\]\[a^2+5a+4=0\]\[(a+1)(a+4)=0\]\[a=-1~~~,~~~~a=-4\]\[x^2=-1~~~~,~~~x^2=-4\]\[x=±~i~~~~,~~~x=±~2i\]

Answer 4

See how I'm doing it, no knowledge besides imaginary numbers and basic algebra.